Joan recieved a discount of $4.80 on a book that originally cost 60$. What was the percent of discount she recieved?

Eight percent — not much eh?  To do the calculation's easy. There are two ways :-

1. Divide the discount by the ticket price and multiply the result by 100 (or just move the decimal places 2 left)
ie 4•80 divide by 60 = •08,
multiply •08 by 100 = 8 (%)
2. Divide the ticket price by 100 and divide the discount by the result
ie 60 divided by 100 = •6      ( one 'percent' of 60 is •6)
divide 4•80 by •6 = 8              ( there are 8 'percents' of 60 in 4•8)

I prefer the second way because it reflects what the question really means:
"How many hundredths (what percent) of 60  are there 4.80?"
Remember that the word percent means hundredths parts.