We start by rewriting \(\frac{4}{\sqrt{(4 - 3x)}}\) as \(4(4 - 3x)^{-\frac{1}{2}}\).

Using the binomial expansion for \((1 - u)^n\), where \(u = \frac{3}{4}x\) and \(n = -\frac{1}{2}\), we have:

\((1 - \frac{3}{4}x)^{-\frac{1}{2}} = 1 + \left(-\frac{1}{2}\right)\left(-\frac{3}{4}x\right) + \frac{\left(-\frac{1}{2}\right)\left(-\frac{1}{2} - 1\right)}{2!}\left(-\frac{3}{4}x\right)^2 + \ldots\)

Calculating each term:

First term: \(1\)

Second term: \(\frac{3}{8}x\)

Third term: \(\frac{27}{128}x^2\)

Multiply the entire expansion by 4:

\(4 \times \left(1 + \frac{3}{8}x + \frac{27}{128}x^2\right) = 4 + \frac{3}{2}x + \frac{27}{32}x^2\)

Simplifying gives:

\(2 + \frac{3}{4}x + \frac{27}{64}x^2\)