Variables:

Let a = Pat's age

Let b = Patrick's age

Given: Pat is 20 years older than his son Patrick.

Means: a = b + 20

Given: In 2 years Pat will be twice as old as Patrick

Means: a + 2 = 2(b + 2)

You have 2 equations.

a = b + 20

a + 2 = 2(b + 2)

Substitute a with b + 20 in the second equation.

a + 2 = 2(b + 2)

b + 20 + 2 = 2(b + 2)

b + 22 = 2(b + 2)

Expand the RHS.

b + 22 = 2(b) + 2(2)

b + 22 = 2b + 4

Subtract b from both sides

b + 22 - b = 2b + 4 - b

22 = b + 4

Subtract 4 from both sides.

22 - 4 = b + 4 - 4

18 = b

Plug this into the first equation to find a.

a = b + 20

a = 18 + 20

a = 38