To find the coefficient of \(x^2\) in the expansion of \((2 + ax)^6\), we use the binomial theorem:

\(\binom{6}{2} \cdot 2^4 \cdot (ax)^2 = 15 \cdot 16 \cdot a^2 x^2 = 240a^2 x^2\)

To find the coefficient of \(x^3\), we have:

\(\binom{6}{3} \cdot 2^3 \cdot (ax)^3 = 20 \cdot 8 \cdot a^3 x^3 = 160a^3 x^3\)

Setting the coefficients equal gives:

\(240a^2 = 160a^3\)

Solving for \(a\), we divide both sides by \(a^2\) (assuming \(a \neq 0\)):

\(240 = 160a\)

\(a = \frac{240}{160} = \frac{3}{2}\)