Given the data, how long is the cell cycle for these cells?

it takes three hours for the nucleus to divide and one hour for the cytoplasm to divide.
after eight hours, the cell will start dividing again.
it takes two hours for the cell to copy its genetic material.

There is no as such fixed time period within which a cell divides. Different cells take different time periods to divide and complete the cell cycle however in human beings a typical cell takes 24 hours to divide while the cells in the intestine complete on life cycle of cell formation in 9-10 hours.

As given in this case

It takes three hours for the nucleus to divide = 3 hours

One hour for the cytoplasm to divide = 2

It takes two hours for the cell to copy its genetic material. = 2 hours

So one cycle of cell division takes place with in (3+2+2) = 7 hours

After 8 hours the same process is repeated and thus the total time taken for division = (7+8+7) = 22 hours

your spelling is a little off : ]