What percent of 60 is 15

15/60 = 1/4 or 25 %

or 
n% x 60 = 15  (the statement you wrote above changed into math)

.60n = 15  What allows me to move the decimal back two places?  Normally you can change a percent to a decimal by moving it back two places.  But if you don't know what the % is, you can move the number you are multiplying by back two places instead.
For example:   37 x .45 = .37 x 45  both = 16.65  - this shows that it doesn't matter which number is moved back two places - the answer will be the same.  You can't move n% back two places (because you can't move a number you don't know back two places) so just move the number you are multiplying by, namely 60, back two place - that is how I got .60

.60n=15
.60    .60          divide both sides by .60

n= 25%