Answer
The force would become 6 times the initial force i.e. $6F$
Work Step by Step
We know that,
$F=k\frac{q_{1}.q_{2}}{r^{2}}$
When the charge of one was doubled and that of the other was tripled, then new force $F_{1}=k\frac{2q_{1}.3q_{2}}{r^{2}}=6F$
The force would become 6 times the initial force.