Which of the following alternatives is grammatically correct?

Concept

A demonstrative adjective must agree in number with the noun it points to. "this/that" are singular and modify a singular noun; "these/those" are plural and modify a plural noun. The noun itself must also carry the correct plural form, and the verb must agree with that subject in number.

Applying it here

• "man" is an irregular noun whose plural is "men" (not "mans").

• Because the people are plural, the sentence needs the plural noun "men," the plural demonstrative "these," and the plural verb "are."

• All these men are gentle. satisfies every requirement: "these" (plural) + "men" (plural) + "are" (plural) all agree.

Contrast with the near-misses

• "All these man are gentle." pairs plural "these" with singular "man" — number disagreement.

• "All this men are gentle." pairs singular "this" with plural "men" — number disagreement.

• "All these mans are gentle." uses the invalid plural "mans" — wrong noun form.

Only the version with "these," "men," and "are" is fully consistent in number.