Let's simplify the expression step by step. We are given the expression \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\).

First, let's simplify the numerator:

\[3(2^{n+1}) - 4(2^{n-1}) = 3(2 \cdot 2^n) - 4(\frac{2^n}{2}) = 6 \cdot 2^n - 2 \cdot 2^n = 4 \cdot 2^n\]

Now, let's simplify the denominator:

\[2^{n+1} - 2^n = 2 \cdot 2^n - 2^n = 2^n\]

Substituting these simplified expressions into the original expression, we get:

\[\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n} = \frac{4 \cdot 2^n}{2^n} = \frac{4}{1} = 4\]

Therefore, the simplified expression is 4.