We can take the days three at a time.
First three days, the daily pattern is 4hrs of work, wages=4*9=$36, 4*2=8 memberships sold, 8*12=$96 commission. The daily total earnings=36+96=$132. Total earnings after 3 days=3*132=$396.
Last three days, the daily pattern is 4hrs of work, wages=4*9=$36, 4*3=12 memberships sold, 12*12=$144 commission. The daily total earnings=36+144=$180. Total earnings after 3 days=3*180=$540.
After 6 days' working Paloma earns 396+540=$936, exceeding the goal of $900.
After 5 days' working she would earn: 396+2*180=$756.
The graph shows accumulated earnings against day number:
It takes 6 days for Paloma to reach her goal of $900 (she actually earns $936).
Her earnings per hour in the last 3 days= 9 (wages) + 3*12 (commission)=$45.
After 5 days' work she has to make up 900-756=$144. If her minimum working time is 1 hr she would need more than 3 hours to reach her goal after 5 days' work, because 756+135=$891. This confirms that she would have to work 6 days.