Which noun does a DETERMINER follow in cases like "this/these"+"year's crops"?

Question

Which of the following are correct and why are they and others aren't?

1. This year's crops are much better.
2. These year's crops are much better.
3. This employees' boss is much better.
4. These employees' boss is much better.

Can I say, "These N. Chomsky's books are amazing!"? And at the same time, could I also say, "This man's books are amazing!".

Generally, I am trying to understand when can one link a determiner to the possessive_noun and when can one link the determiner to the possessed_noun.

In "year's crops", "year's" is possessive noun and "crops" is the possessed noun.

Answer 1

You use "this" for singular and "these" for plural. Therefore, 1 and 4 are correct, 2 and 3 are incorrect.

This / these refers to year and employees, not to crops and boss.

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"These N. Chomsky's books are amazing!"

should be:

"These books by N. Chomsky are amazing!"

or:

"N. Chomsky's books are amazing!"

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Generally, I am trying to understand when can one link a determiner to the possessive_noun and when can one link the determiner to the possessed_noun.

That depends on what yo want to say. You need to be careful not only about the grammar, but also to the logical meaning of the sentence.