Answer
In pair (1) and pair (2), if the separation between the particles is increased, the potential energy increases.
In pair (3) and pair (4), if the separation between the particles is increased, the potential energy decreases.
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:
$U_4 = \frac{1}{4\pi~\epsilon_0}~\frac{(-6q)(-2q)}{r}$
$U_4 = \frac{1}{4\pi~\epsilon_0}~\frac{12q^2}{r}$
In pair (1) and pair (2), if the separation between the particles is increased, the magnitude of $U$ decreases as $U$ becomes less negative. Therefore, the potential energy increases.
In pair (3) and pair (4), if the separation between the particles is increased, the magnitude of $U$ decreases as $U$ becomes less positive. Therefore, the potential energy decreases.
