Formula use:

\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3

Explanation

Here, given expression is :
\left(4x-3y\right)^3-3.\left(4x-3y\right)^2\left(4x-2y\right)+3.\left(4x-3y\right)\left(4x-2y\right)^2-\left(4x-2y\right)^3
Let,
\left(4x-3y\right)=a
\left(4x-2y\right)=b
Now, Simplify the expression :
\left(4x-3y\right)^3-3.\left(4x-3y\right)^2\left(4x-2y\right)+3.\left(4x-3y\right)\left(4x-2y\right)^2-\left(4x-2y\right)^3
\rightarrow a^3-3a^2b+3ab^2-b^3
\rightarrow\left(a-b\right)^3
\rightarrow\{\left(4x-3y\right)-\left(4x-2y\right)\}^3
\rightarrow\left(4x-3y-4x+2y\right)^3
\rightarrow\left(-y\right)^3
\therefore{-y}^3
Ans: {-y}^3\ .