"My brother is listening to me."

Translation: मेरा भाई मेरी बात सुन रहा है।

[Philip986658]

I was confused, trying to find a 'mujhe', rather than 'meri baat'.

[Mark347251]

Me too, at first. But he's not listening to you -- he's listening to what you're saying (!)

[Mark347251]

So, then I was looking for a 'ko' to follow baat...

[whimslcott]

So why is it मेरी but रहा even though both are being gendered by बात? Or are they not being gendered by बात?

[Zerenei]

मेरा भाई मेरी बात सुन रहा है। (Literally: My brother is listening to my talk, as in listening to the things I am saying.)
बात is feminine, hence मेरी बात.
Without an object, the sentence is मेरा भाई सुन रहा है। रहा because he is your brother, masculine. The object (मेरी बात) does not depend on the subject of the sentence.
मैं उसका सेब खाता हूँ = I eat his/her apple. मैं उसकी किताब पढ़ता हूँ = I read his/her book. मैं उसके कुत्ते देखता हूँ = I see his/her dogs.

[xyfell]

Why couldn't the answer be:
मेरी मेरा भाई बात सुन रहा है

[ksriram]

You are taking the free word order part of Hindi too literally. It is more like free phrase order. Words within a phrase have to stay together and in order. This sentence has three phrases:
1. मेरा भाई
2. मेरी बात
3. सुन रहा है
You can put them in any order you want and the sentence would still mean the same thing. But you can't split the phrases themselves. Or change the order of words within the phrase (actually you can to a limited extent). Also if it is a compound sentence with multiple clauses, the phrases have to stay within their clause.

[pinki296289]

Its ok..but mujhe is better
Than बात