"Why do you not talk to me?"
Translation:तुम मुझसे बात क्यों नहीं करते?
In the absence of the negation, क्यों has to go before the verb in the sentence. In this case, करना (to do) is the verb though बात करना (to talk) can also be considered a composite verb. This means both 'बात क्यों करते हो' and 'क्यों बात करते हो' are correct as is 'बात करते क्यों हो' (where क्यों is before होना-to be). These different versions have subtle variations in meaning (like stressing on different words while speaking). For example, 'तुम मुझसे बात करते क्यों हो' is closer in meaning to 'Why do you bother talking to me?'.
The negation नहीं which can be thought of as modifying the verb HAS to be right adjacent to the verb. It is usually present before the verb but sometimes, it can also be placed right after the verb when you want to emphasise the negation. Again for verbs such as बात करना, नहीं can go before बात or करना but it is more common to place it before करना.
From what I've said above, you can see that though the given sentence is the most natural, there are a bunch of other grammatically correct sentences you can get by changing the word order,