Learn Italian: Sua cognata è molto simpatica. - His sister-in-law is very nice.

Normally, Italian requires a definite article (like "the") before possessive words, as in la sua casa (his/her house). However, there is a special rule: we drop the article for singular family members. Because cognata (sister-in-law) is a singular family member, it is simply sua cognata, not la sua cognata.

The translation says "his", but isn't sua feminine?

Yes, sua is feminine! In Italian, possessive words match the gender of the person or thing being talked about, not the owner. Since cognata is a feminine noun, we must use sua, even if the person who has the sister-in-law is a man. Sua cognata can mean either "his sister-in-law" or "her sister-in-law" depending on the context.

Why doesn't molto change to molta to match the feminine word cognata?

When molto is used to mean "very" (describing how nice she is), it acts as an adverb, which means it never changes its ending. It stays exactly like this: molto simpatica. It only changes to match a word's gender and number when it means "a lot of" or "many" right before a noun (like molta pasta).

What kind of "nice" does simpatica mean?

Simpatica (and its masculine form, simpatico) describes someone who is pleasant, likable, and friendly to be around. It is used to describe someone's personality, not their physical appearance.