SOLUTION: I have twenty four coins out of the twenty four coins how many are nickels with the total of $4.80

There are many answers.

You could have 3 nickels like this:

17 quarters = $4.25
 4 dimes        .40
 3 nickels  =   .15
-------------------
24  coins   = $4.80 
           
Or you could have 6 nickels like this:

18 quarters = $4.50
 6 nickels  =   .30
-------------------
24  coins   = $4.80

Or you could have 0 nickels at all

19 quarters = $4.75
 5 pennies  =   .05
-------------------
24  coins   = $4.80

If half dollars or dollar coins are allowed there are many many more ways.

Here is a way with 4 nickels if you use 8 half dollars.

 8 half dollars = $4.00
 2 quarters     =   .50
 4 nickels      =   .20
10 pennies      =   .10
-----------------------
24 coins        = $4.80

If you can use dollar coins, here's a way to have 17 nickels.

 3 dollar coins = $3.00
 1 half dollar  =   .50
 1 quarters     =   .25
 2 dimes        =   .20
17 nickels      =   .85
-----------------------
24 coins        = $4.80 

Edwin