That's because you have both equation wrong.  Also 54 should be 64. It comes
out fractions with 54, so it must have been 64.

To get money you can't add coins to coins.  

You have p+d=54.  Not only should the 54 be 64, but

pennies + dimes = cents

is senseless, it's like

apples + oranges = bananas.

Your equation must not be 

copper coins + silver coins = amount of money.

You must have

amount of money + amount of money = amount of money 

cents + cents = cents.

p pennies is worth p cents,

d dimes is worth 10p cents.

So your first equation is

p + 10d = 64, not p+d=64, and certainly not p+d=54

You also interpreted this clause wrong:

Notice these three examples:

If she had 2 dimes, she would have 12 pennies.
If she had 3 dimes, she would have 18 pennies
If she had 5 dimes, she would have 60 pennies.

So to get the number of pennies you must mutiply the number of dimes by 6.
So you have it backwards.

Its p=6d, not d=6p

So the two equation should be:

p+10d=64
p=6d

Substitute 6d for p in the first equation

6d+10d=64
   16d=64

divide both sides by 16

     d=4

Then since p=6d, p=6(4) = 24

So there are 3 dimes and 24 pennies.

Edwin