Y = square root of x / 3 - x. For which values of x will y be real?

Please use parentheses, because I can't tell whether you mean:

y = \sqrt{\frac x 3 - x}

Or:

y = \sqrt {\frac x 3} - x

Or:

y = \frac {\sqrt x} 3 - 4

In any event, you need to determine fior what values of x the value inside the square root sign is non-negative. Can you do that?