Kids grow up fast these days!

Let Percy's age be x.

Lily's age = Percy's age + 4

Lily's age = x + 4

Lily's age + Percy's age = 40

x + x + 4 = 40

2x = 36

x = 18

Hence Percy's age is 18

Let $x$ be the number of years from now so that the sum of their ages is $40$ . Then

$(12+x)+(8+x) = 40$

$12+x+8+x=40$

$20+2x=40$

$2x=20$

$x=10$

So at that time, Percy must be $10+8=18$ years old.

When Percy's age is $x$ , Lily's age is $x + 4$ .

$x + x + 4 = 40$

$2x + 4 = 40$ | - 4

$2x = 36$ | : 2

$x = 18$

When the sum of Lily's and Percy's ages is fourty, Percy will be 18.

$Lily\quad is\quad twelve\quad years\quad old\quad and\quad her\quad brother,\quad Percy,\quad is\quad eight.\\ Mean\quad Percy\quad is\quad 4\quad year\quad younger\quad than\quad his\quad sister.\\ When\quad Sum\quad of\quad thier\quad ages\quad is\quad equal\quad to\quad 40\\ Lily+Percy=40\\ 22+18=40\\ The\quad answer\quad is\quad \boxed { 18 }$

easier solution : sum of ages now=20(12+8) , req sum of ages =40 (12+x+8+x) diff=20 =2x ; x=10 .. so after 10 years age of Percy=8+10=18