this week.

[Alanmo]

His older son said that he was not responsible for the laundry this week.

Is this sentence ok? If not,why?

The sentence seems fine to me. I think the problem lie in "this week"

Thank you

[Casiopea]

It's OK but a tad ambiguous. Try,

His older son said that he was not responsible for this week's laundry.

[Casiopea]

Here's the ambiguity:

(a) He said ... this week; i.e., he said it this week
(b) the laundry this week; i.e., this week's laundry

[Alanmo]

Thank you,

[Casiopea]

You're most welcome, Alanmo.