let p = son Patrick's age
then father Pat's age is (p + 20)
in 8 years, son Patrick's age will be p + 8
in 8 years, Pat's age will be (p + 20) + 8
If Pat will be twice as old as son Patrick in 8 years we can write the following equation:
(p+20) + 8 = 2(p+8) and solve for p
p+28 = 2p + 16
12 = p
This means that patrick is 12 years old
And pat is 32 years old