To find the total amount he should charge for the coloring service, we need to add up the cost of the products, the cost of his time, and the profit he wants to make.
First, we need to convert the time he spends applying the product to hours. 15 minutes is a quarter of an hour, so the total time is 1.25 hours.
The cost of his time is $25 per hour, so the cost of his time for the coloring service is:
$25/hour * 1.25 hours = $31.25
The cost of the products is $32.
Adding the cost of his time and the cost of the products, we get:
$31.25 + $32 = $63.25
To add 20% to the total amount for profit, we need to multiply $63.25 by 1.2:
$63.25 * 1.2 = $75.90
Therefore, the hair stylist should charge $75.90 for the coloring service.