Okay, here we have this:
Considering that she has has $4 and she has 2 more quarters than dimes.
We obtain the following:
The number of dimes=x
The number of quarters=y=x+2
So we have the following equation:
$4=$0.10x+$0.25y
4=0.10x+0.25(x+2)
4=0.10x+0.25x+0.5
3.5=0.35x
x=10
Now, let's replace x=10 in y:
y=x+2
y=10+2
y=12
Finally we obtain that Taylor has 10 dimes and 12 quarters.