Twice one number is 20 more than another number. one fourth the first number is 2 less than one fourth the second number. find the numbers.

Let x and y are 2 numbers
2x = 20 +y (1st equation)
1/4x = 1/4 y - 2 (2nd equation)

2x = 20 +y (1st equation) 
y = 2x -20 replace this to the 2nd equation

1/4x = 1/4 (2x-20) - 2
1/4x = 1/2x - 5 - 2
1/4x = 1/2x - 7
1/4x - 1/2x = -7
1/4x - 2/4x = -7
-1/4x = -7
x = -7 * -4
x = 28

y = 2x -20
y = 2(28) - 20
y = 56 -20
y =36

Proof:

2x = 20 +y (1st equation)
2(28) = 20 + 36
56 = 56

1/4x = 1/4 y - 2 (2nd equation)
1/4(28) = 1/4(36) -2
7 = 9-2
7 = 7

Numbers are 28 and 36