If we call Ralph's earnings (in dollars) E and the time he spends working (in hours) t, we can model those earnings with the equation
E = 32 + 33t
This fits with the question statement because after 0 hours, the equation states
E = 32 + 33(0) = 32
Which represents the initial fee he charges.
Here, we're given his earnings - E = 197 - and we want to find what t has to be to get there. Specifically, we want to solve the equation 197 = 32 + 33t for t.
Subtracting 32 from either side, we find
197 - 32 = 32 + 33t - 32
165 = 33t
And dividing either side by 33 leaves us with
5 = t
So, it takes Ralph 5 hours to earn $197.