Help me count my children

Let the numbers of sons and daughters be $x$ and $y$ respectively.

Then, from the $2$ given condition we get, $x+1=y$ $2(x-1)=y$

Solving them we get, $\color{#0C6AC7} {\boxed {(x, y) \equiv (3,4)}}$

Let the total number of daughters be $x$

The number of sisters my daughter has is $x-1$ which is equal to the total number of sons I have.

Let the total number of sons be $x-1$

Each son therefore has ( $x-1-1$ ) brothers, that is, $x-2$

as well as $2(x-2)$ sisters which equals the total number of daughters I have

Since the total number of daughters I have is represented by $x$

We have an equation, $x=2(x-2)$

$x=2(x)-4$

$x=4$

Therefore the total number of daughters I have is 4

It implies that the total number of sons I have is 3