How many children are there?

let $C$ = sum of the children's ages, $P$ = sum of the parent's ages and $x$ = number of children

at present:

$C=\dfrac{1}{2}P$ or $P=2C$

2 years ago:

$P-2(2)=3(C-2x)-28$ $\implies$ $P-4=3C-6x-28$ $\implies$ $P=3C-6x-24$ but: $P=2C$ ,

therefore it becomes $2C=3C-6x-24$ $\implies$ $-C=-6x-24$ $\color{#D61F06}(1)$

20 years from now:

$C+20x=P+20(2) + 20$ $\implies$ $C+20x=P+40+20$ $\implies$ $C+20x=P+60$ but: $P=2C$ ,

therefore it becomes $C+20x=2C+60$ $\implies$ $-C=-20x+60$ $\color{#D61F06}(2)$

Subtracting $\color{#D61F06}(2)$ from $\color{#D61F06}(1)$ , we get

$0=14x-84$ $\implies$ $14x=84$ $\implies$ $\boxed{x=6}$