This site is about Wolfram Technologies. And while you do mention it, your actual question is not about Wolfram Technologies but about doing math by hand. You should not be asking this questions on this forum, but find another dedicated place, for example HERE. Both Wolfram|Alpha and Wolfram Language can give you the final answer though.
FunctionDomain[(4 - x^4)^(1/4), x]
NumberLinePlot[FunctionDomain[(4 - x^4)^(1/4), x], {x, -2, 2}]
Plot[(4 - x^4)^(1/4), {x, -2, 2}]