To express \(4x^2 - 12x\) in the form \((2x + a)^2 + b\), we start by expanding \((2x + a)^2\):

\((2x + a)^2 = 4x^2 + 4ax + a^2\).

We want this to match \(4x^2 - 12x\), so we equate the coefficients:

\(4a = -12\) which gives \(a = -3\).

Substitute \(a = -3\) back into \((2x + a)^2\):

\((2x - 3)^2 = 4x^2 - 12x + 9\).

Now, compare \(4x^2 - 12x + 9\) with \(4x^2 - 12x\):

\(4x^2 - 12x = (2x - 3)^2 - 9\).

Thus, \(b = -9\).