You would have worked 6 hours as lifeguard and 8 hours as cashier.
8(14 - y) + 6y = 96
112 - 8y + 6y = 96
112 - 2y = 96
-2y = -16
y = -16/-2 = 8
You worked 8 hours as a cashier. since the total hours worked is 14 we know you worked as a lifeguard for 6 hours.