Kids grow up fast these days!

Let the given consition be satisfied in $x$ years.
Then $12 + x + 8+ x = 40\\ 20 + 2x = 40\\ 2x = 20\\ x = 10$

So, $10$ years hence, Lily's age would be $12 + 10 = \color{#69047E}{\boxed{22}}$ .

Lily-Percy=4 Lily+percy=40 adding these 2 equations 2Lily=44 Lily=22

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

$x = 10$

their ages when summed up after 10 years will be 40.

lily's age is $12 + 10 = \boxed{22}$

lets assume that the amount of years that go by until the sum of their ages is 40 is equal to y then lily's age would be y+12 and percy's age would be y+8 and the sum of their ages then is 40 so y+12+y+8=40 2y+20=40 y=10 so lily's age then is 10+12=22