(2x²+y)⁶?
If so, the expansion would be:
(2x²)⁶+6(2x²)⁵y+15(2x²)⁴y²+20(2x²)³y³+15(2x²)²y⁴+6(2x²)y⁵+y⁶.
The coefficient of x⁶ and y³ is 20(2³)=160.
If (1-y³)(2x²+y)⁶=(1-y³)(...+20(2x²)³y³+...)=...-160x⁶y⁶-...
The coefficient of y⁶ is therefore -160.
If (1-3y)(2x²+y)⁶=(1-3y)(...+12x²y⁵+...)=...-36x²y⁶-...
The coefficient of y⁶ is therefore -36.
Your question has a lot of missing text so it’s just a guess at what the question means.