First, find \(gf(x)\):

\(gf(x) = g(f(x)) = g(2x - 3) = (2x - 3)^2 + 4(2x - 3)\)

Expand \((2x - 3)^2\):

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

Expand \(4(2x - 3)\):

\(4(2x - 3) = 8x - 12\)

Combine terms:

\(gf(x) = 4x^2 - 12x + 9 + 8x - 12\)

\(gf(x) = 4x^2 - 4x - 3\)

Set \(gf(x) = p\):

\(4x^2 - 4x - 3 = p\)

Rearrange to form a quadratic equation:

\(4x^2 - 4x - 3 - p = 0\)

For the equation to have two equal roots, the discriminant must be zero:

\(b^2 - 4ac = 0\)

Here, \(a = 4\), \(b = -4\), \(c = -3 - p\).

Calculate the discriminant:

\((-4)^2 - 4 \times 4 \times (-3 - p) = 0\)

\(16 - 16(-3 - p) = 0\)

\(16 = 16(3 + p)\)

\(16 = 48 + 16p\)

\(16p = 16 - 48\)

\(16p = -32\)

\(p = -2\)

However, according to the mark scheme, \(p = -4\).