If the difference of two numbers is 48 and one number is 4 times the other number then what are the two numbers?

First, put the problem into equation form:
x - y = 48
4y = x

Now use substitution:
x - y = 48
4y - y = 48
3y = 48
y = 16

Finally, solve for x:
4y = x
4(16) = x
64 = x

One number is 64, and the other is 16.
If you check, you will see that these two numbers satisfy their description.