Solution:

If we define the signals,

$x_1(n)=2^n u(n)\\ $

$x_2(n)=3^n u(n)\\ $

then x(n) can be written as

$x(n)=3 x_1(n)-4 x_2(n)\\ $

According to (3.2.1), its z-transform is

$X(z)=3 X_1(z)-4 X_2(z)\\ $

From (3.1.7) we recall that,

$ \alpha^n u(n) \stackrel{\vdots}{\longleftrightarrow} \frac{1}{1-\alpha z^{-1}} \quad \text { …