No, 10 gallons is NOT larger than 60 quarts.
An easy way to do this is to find what quarts is when converted into gallons, or you can go the other way and convert gallons into quarts.
1 gallon = 0.25 quarts, so we need to do → 0.25 × 60 = 15 gallons.
So, 10 gallons is NOT larger than 15 gallons.