[tex]\bf \begin{cases}
s=\textit{area of the square}\\
h=\textit{area of the hexagon}
\end{cases}
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\textit{38 less than 2 times the area of a hexagon}\implies \boxed{s}=2h-38
\\\\\\
\textit{we also know that their sum is }\implies s+h=46
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\boxed{2h-38}+h=46\implies 3h=46+38\implies 3h=84
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h=\cfrac{84}{3}\implies h=28[/tex]
what's the area of the square? well, s = 2h - 38.