imc

Let $x$ be the number of the children and the mom. The father, who is $48$, plus the sum of the ages of the kids and mom divided by the number of kids and mom plus $1$ (for the dad) = $20$. This is because the average age of the entire family is $20.$ This statement, written as an equation, is: $$\frac{48+16x}{x+1}=20$$ $$48+16x=20x+20$$ $$4x=28$$ $$x=7$$ $7$ people - $1$ mom = $6$ children. Therefore, the answer is $\boxed{6}$