Answer
We can rank the pairs according to their electric potential energy:
$U_3 = U_4 \gt U_1 = U_2$
Work Step by Step
We can write a general expression for the electric potential energy of a system of two charged particles:
$U = \frac{1}{4\pi~\epsilon_0}~\frac{q_1~q_2}{r}$
We can find an expression for the electric potential energy of the pair (1) system:
$U_1 = \frac{1}{4\pi~\epsilon_0}~\frac{(-2q)(+6q)}{r}$
$U_1 = -\frac{1}{4\pi~\epsilon_0}~\frac{12q^2}{r}$
We can find an expression for the electric potential energy of the pair (2) system:
$U_2 = \frac{1}{4\pi~\epsilon_0}~\frac{(+3q)(-4q)}{r}$
$U_2 = -\frac{1}{4\pi~\epsilon_0}~\frac{12q^2}{r}$
We can find an expression for the electric potential energy of the pair (3) system:
$U_3 = \frac{1}{4\pi~\epsilon_0}~\frac{(+12q)(+q)}{r}$
$U_3 = \frac{1}{4\pi~\epsilon_0}~\frac{12q^2}{r}$
We can find an expression for the electric potential energy of the pair (4) system:
$U_4 = \frac{1}{4\pi~\epsilon_0}~\frac{(-6q)(-2q)}{r}$
$U_4 = \frac{1}{4\pi~\epsilon_0}~\frac{12q^2}{r}$
We can rank the pairs according to their electric potential energy:
$U_3 = U_4 \gt U_1 = U_2$
