Is my usage of the word “forthcoming” correct?

Question

I truly appreciate your forthcoming by bringing to my notice about the noise I am causing.

or

I truly appreciate you forthcoming by bringing to my notice about the noise I am causing.

Answer 1

Your sentence is ungrammatical in a couple of respects.

forthcoming is an adjective that means "candid". So you would have to say

I appreciate you being forthcoming

or

I appreciate that you were forthcoming

Second, we "bring something to someone's notice". bring is a transitive verb that has a direct object, and thus the prepositional phrase "about the noise" is wrong.

... by bringing the noise I was making to my notice

... by bringing to my notice the noise I was making

Answer 2

Forthcoming has various meanings none of which make sense here. I think you mean 'coming forward'. You could say "I truly appreciate your coming forward and bringing the noise I am causing to my notice."