Learn Croatian: Uzmi tu kravatu i moj kaput.

In Croatian, distance matters! tu is the accusative feminine form of taj, which means 'that one right near you' (the listener). If the tie were further away from both of you, you would use onu (from onaj - that one over there).

Why do we say tu kravatu instead of ta kravata?

The tie is the direct object of the action 'take' (uzmi), so it must be in the accusative case. For feminine words ending in -a, the ending changes to -u. The demonstrative pronoun 'that' (ta) must match the noun, so it also changes to tu.

If 'that tie' is in the accusative case, why didn't 'my coat' (moj kaput) change its ending?

moj kaput actually is in the accusative case here! In Croatian, masculine nouns that are inanimate (objects, not living beings) look exactly the same in the accusative case as they do in the nominative (dictionary) form. Since a coat isn't alive, kaput doesn't change endings here.

What is the dictionary form of the command uzmi?

The dictionary form (infinitive) is uzeti (to take). uzmi is the imperative form, which you use to give a direct command or instruction to one person.