"that" with embedded questions?

[dihen]

Is it true that "Who do you think that likes me" is wrong, but "Who/Whom do you think that I like" is correct? And it seems that omitting the "that" is also correct, so is it better to simply omit the "that"?

[david_werrett]

In this case the use of 'that' is unnecessary. The question sould begin 'Whom'.

[Tdol]

I think you can use who/whom- the distinction between subject and object is much less marked these days with these words, and the majority of native speakers use 'who':
From Google:
Who do you like? 146,000
Whom do you like? 1,680
I don't agree with those that regard 'whom' as dead or moribund, but it's use in such questions is in decline, though after prepositions it seems to be doing well.

[dihen]

How can I correct "You think why he did this?"? I can't use "Why do you think he did this?" nor "For what do you think he did this?", because the meaning would change. I know I can use "What do you think he did this for?", but then the sentence would end with a preposition.

[Coffa]

You say the meaning would change. I am actually unsure which meaning you wish to convey. Your last sentence is perfectly OK. The prohibition that sentences must not end with a proposition is a myth. This has been recognised by grammaticians for hundreds of years. It is a fallacy propagated by English teachers who rely solely on the misinformation propagated by their own teachers.

[dihen]

You say the meaning would change. I am actually unsure which meaning you wish to convey. Your last sentence is perfectly OK. The prohibition that sentences must not end with a proposition is a myth. This has been recognised by grammaticians for hundreds of years. It is a fallacy propagated by English teachers who rely solely on the misinformation propagated by their own teachers.

I was saying that "Why do you think he did this?" may have two different meanings.

for example:
"[Why] do you [think] he did this?" ("why" modifies "think")
"[Why] do you think he [did] this?" ("why" modifies "did")

the same can apply to the adverbs, "how", "when", "where", and almost any adverbial that contains the words "what", "how", or "which"

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Would I sound like a foreigner if don't use WH-movement, like this?

saying "You think who saw me?" instead of "Who do you think saw me?" (as a direct question, not an echo question)

and saying "You think I saw who(m)?" instead of "Who(m) do you think I saw?" (again, as a direct question, not an echo question)

By the way, I personally think that WH-movement makes certain sentences harder to understand because in a sentence like "Who do you want to help you?" the part "who do you want to help" is still a complete sentence.

[Tdol]

"[Why] do you [think] he did this?" ("why" modifies "think")
"[Why] do you think he [did] this?" ("why" modifies "did")

I'm not sure of this- the question is asking an opinion about the motive, not the motive for me.

[Casiopea]

One way to get rid of the ambiguity is to move the subject-verb pair closer to the adverb:

[a] Why did he do this do you think?
[b] Why do you think he did this?

Is it true that "Who do you think that likes me" is wrong

Yes. It's ungrammatical. "Who do you think" functions as the subject of the verb "likes":

Who do you think likes me?

Adding in "that" creates an adjectival clause:

Who do you think *that likes me? <ungrammatical>

Adjectival clauses modifies nouns, not verbs. Above "that likes me" modifies the verb "think". Below, it modifies the noun "person":

Who is the person that likes me? <grammatical>

"Who/Whom do you think that I like" is correct?

Yes. It's grammatical. "that I like" is a clause - it has a subject and a verb - and it functions as the object of the verb "think"; e.g., I think (that) . . . Cf. "that likes me". 'that' functions as the subject there.

And it seems that omitting the "that" is also correct, so is it better to simply omit the "that"?

It's possible to omit "that" if it functions as a conjunction:

Who do you think (that) I like? <grammatical>

"that" joins the subject-verb units "you think" and "I like".

Compare,

Who do you think *that likes me? <ungrammatical>

"that" joins the subject-verb unit "you think" with a verb-object unit "likes me". They are not the same structurally.

Hope that helps.

[dihen]

Isn't the structure like this (see below), but for some mysterious reason, English doesn't allow the "that-trace effect"? Or am I wrong? I even think that although adding the "that" would make the sentence ungrammatical, but it actually makes the meaning more clear.

"(1)Who (2)do (3)you (4)think (5)that (6)__ (7)likes (8)me?"

1-(moved subject of the subordinate clause)
2-(inverted verb)
3-(subject of main clause)
4-(the second verb of the main clause)
5-{the complementizer (subordinating conjunction)}
6-(original position of the subject of the subordinate clause)
7-(verb of the moved subject "who")
8-(object of the subordinate clause)

[Casiopea]

If we view "thinks that" as a unit, like this,

Do you think that Max likes me?

then moving Max out of its clause and changing it to Who produces,

Who do you think that *likes me? <no subject, overt or covert>

The problem: "that" should function as a conjunction in that context, but it doesn't meet the requirements. It joins a subject-verb pair "you think" with a subject-less verb phrase "likes me".

Do You think *that likes me? <conjunction; ungrammatical>

Substantive-wise,

Do you think that [animal] likes me? <nominal; grammatical>

In short, "that" doesn't have a referential function here, structural or otherwise. That's why it's optional:

Do you think that Max likes me?

Below, the structural environment changes. WH-Max leaves a trace.

Who do you think trace likes me.

Note that, a trace is a structural anchor or place holder. It's not PRO.

Hope that helps.