Given that the progression is arithmetic, the common difference \(d\) is 12.

The first term is \(4x\) and the second term is \(x^2\).

Therefore, the common difference equation is:

\(x^2 - 4x = 12\)

Rearranging gives:

\(x^2 - 4x - 12 = 0\)

Solving this quadratic equation using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 1\), \(b = -4\), \(c = -12\):

\(x = \frac{4 \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot (-12)}}{2 \cdot 1}\)

\(x = \frac{4 \pm \sqrt{16 + 48}}{2}\)

\(x = \frac{4 \pm \sqrt{64}}{2}\)

\(x = \frac{4 \pm 8}{2}\)

\(x = 6\) or \(x = -2\)

For \(x = 6\), the third term is \(x^2 + 12 = 6^2 + 12 = 48\).

For \(x = -2\), the third term is \(x^2 + 12 = (-2)^2 + 12 = 16\).