To check any "solving" exercise, plug your solution back into the original equation:
. . . . .\(\displaystyle x^{\frac{1}{4}}\,+\,2\,=\,4\)
. . . . .\(\displaystyle (16)^{\frac{1}{4}}\,+\,2\,\begin{array}{c}?\\=\end{array}\,4\)
. . . . .\(\displaystyle 2\,+\,2\,\begin{array}{c}?\\=\end{array}\,4\)
. . . . .\(\displaystyle 4\,=\,4\)
Your solution "checks". Good work!
Eliz.