It's a place where/(that) you can learn to make cakes.

[sitifan]

It's a place ____ you can learn to make cakes.
(A) that
(B) what
(C) which
(D) where
Source: Hanlin English Workbook, Book 6, page 19.

The answer is option D. Is option A also acceptable?

 

[emsr2d2]

No. Only "where" or "at which" fit there.

 

[5jj]

Also: It's a place (that) you can learn to make cakes at.

 

[sitifan]

We need a place where/(that) we can stay for a few days. (My bold.)
Source: Practical English Usage, by Michael Swan, section 237.7.

It's a place where/(*that) you can learn to make cakes. (My bold.)
Source: Hanlin English Workbook, Book 6, page 19.

In the first quotation, where can be replaced by that or dropped.
In the second quotation, where cannot be replaced by that or dropped.
What makes the difference between them?

 

[Tarheel]

In the first quotation, where can be replaced by that or dropped.

I don't agree.

 

[sitifan]

Practical English Usage, Fourth Edition (Fully Revised International Edition), by Michael Swan has this sentence under subsection 237 relatives: advanced points:

We need a place (that) we can stay for a few days. (BUT NOT We need a house we can stay for a few days.)

What PEU is saying here is that relative adverb where after place can be replaced by that or dropped in an informal style.

But The Cambridge Grammar of the English Language (Page 1053) by H&P begs to differ:

Relatives introduced by where, by contrast, do not in general alternate with the non-wh type except where the antecedent is a very general noun such as place:
[61] i This is much better than the hotel [where we stayed last year].
ii This is much better than the place [where/(?that) we stayed last year].
The ‘?’ annotation in [ii] applies to the version with that (?the place that we stayed last year); the bare relative (the place we stayed last year) is more acceptable.

https://english.stackexchange.com/questions/593418/using-place-that-instead-of-place-where

 

[Tarheel]

In a very informal style, the relative pronoun can be dropped.

I will never forget the day I first met Jane.

I wouldn't use a relative pronoun there in the first place. Therefore, there would be nothing to "drop".

 

[Tarheel]

You may come any time you are free.

The same with that one.

I'm not sure what is meant by "very informal style". To me it's just ordinary conversation.

 

[jutfrank]

It's a place where/*(that) you can learn to make cakes. (My bold.)
Source: Hanlin English Workbook, Book 6, page 19.

In the second quotation, where cannot be replaced by that or dropped.

It's a place ____ you can learn to make cakes.
(A) that
(B) what
(C) which
(D) where
Source: Hanlin English Workbook, Book 6, page 19.

The answer is option D. Is option A also acceptable?

You've just told us that according to the writers and publishers of Hanlin English Workbook, option A is not acceptable, so I imagine that the authority who has told you to use Hanlin English workbook agrees.