1
× My mother is very good at cook.
√ My mother is very good at cooking.
If we use a verb after a preposition, we must use the -ing form of the verb.
2
× I have many cousins, and I have a very good relationship with they.
√ I have many cousins, and I have a very good relationship with them.
After a preposition, we use an object pronoun (me, you, him, her, it, you, us, them). ‘Is this for me?’ ‘I like talking about him.’ ‘I am tired of them.’