The ratio of the units digit to the tens digit of a two-digit number is one-half. the tens digit is two more than the units digit. find the number.

The number is 42.

Let xy be the number.  x is the tens digit, y is the units digit.  The ratio of the units digit to the tens digit, y/x, is 1/2.  This gives us the proportion

y/x = 1/2

The tens digit is 2 more than the units digit; x = y+2; substituting in our proportion we have
y/(y+2) = 1/2

Cross multiply:
y*2 = (y+2)*1
2y = y+2

Subtract y from each side:
2y - y = y+2-y
y = 2

x = y+2
x = 2+2
x =4 

xy = 42