The way I attempted to solve it.

Total distance = 28 cm
Rate = 2 cm per 0.5 hour = 4 cm per hour

Time to cover this distance: T = 28/4 = 7 hours

Now, the frog takes a break every couple of hours for half an hour which means, during these 7 hours, it must have taken 3 half-hour breaks that is 0.5*3 = 1.5 hours; and slipped back 1 cm during each break (3 cm for all three breaks).

Finally, to cover this 3 cm gap, the time taken will be: T = 3/4 = 0.75 hours

Adding all times together = 7 (time for given rate without break) + 1.5 (3 half-hour breaks) + 0.75 (time taken to cover gaps created during each break) = 9.25 hours