Let x be the units' digit and y be the tens' digit. Thus the number is 10y + x.
The units digit is 3 greater than the tens' digit: x = 3 + y (1)
The integer is 4 times as large as the sum of its digits: 4(x+y) = 10y + x (2)
Substitute 1 to 2: 4(3 + y + y ) = 10y +3 + y
4(3 +2y ) = 11y +3
12 + 8 y = 11y +3
y = 3
x = 3 + 3 = 6
Thus the integer is 10(3) + 6 = 36