Learn Croatian: Razgovaram s tvojom bučnom braćom. - I am talking with your noisy brothers.

This is because braća (brothers) is a collective noun. In Croatian, collective nouns ending in -a (like braća, djeca, gospoda) act grammatically like feminine singular nouns. Because of this rule, any adjectives or pronouns attached to them must take feminine singular endings, even though the physical people are male.

What case is the phrase tvojom bučnom braćom in, and why?

It is in the instrumental case. The preposition s (with) requires the instrumental case when it refers to doing an action in someone's company, such as talking with someone (razgovarati s).

How exactly do we form the instrumental of braća?

Since braća declines like a regular feminine singular noun ending in -a (like žena), you drop the -a and add the standard instrumental ending -om, giving us braćom. The pronoun and adjective follow the same feminine singular pattern to match it: tvojom bučnom.

Since braća uses feminine singular adjectives, what would happen to the verb if braća was the subject?