When there is a discount, you multiply the percent by the original price and subtract that amount from the original price. Sales tax is kinda the same, except you add the amount rather than subtract.
15% = 0.15
0.15 • 120 = 18
This means the discount was for $18 off the sneakers.
120 - 18 = 102
So the price of the sneakers without tax with the discount was $102.
8% = 0.08
0.08 • 102 = 8.16
This means the sales tax for the sneakers was 8.16. Add this to the price.
102 + 8.16 = 110.16
So the total price Nick paid for the sneakers was $110.16.