Had all coins be dimes, the 32 coins would worth $3.20.


The difference $6.20 - $3.20 = 300 cents is due the fact that we counted quarters as cents - so we need to replace 

some number of dimes by quarters in our counting.


Each replacement will diminish the difference of 300 cents by 25-10 = 15 cents.


So, we need to make  = 20 replacements.


Thus the collection contains 20 quarters and 32-20 = 12 dimes.


Answer.  The collection contains 20 quarters and 12 dimes.