[tex]\frac{1}{2}(\frac{1}{3}w+4)+6=10\\\\
\frac{1}{6}w+\frac{4}{2}+6=10\\\\
\frac{1}{6}w+2+6=10\\\\
\frac{1}{6}w+8=10\ \ \ |Subtract\ 8\\\\
\frac{1}{6}w=2\ \ \ |Multiply\ by\ 6\\\\
\boxed{w=12}\\\\\\
-5(h+4)=12\\\\
-5h-20=12\ \ \ |Add\ 20\\\\
-5h=32\ \ |Divide\ by\ -5\\\\
h=-\frac{32}{5}=-6\frac{2}{5}\\\\
\boxed{h=-6\frac{2}{5}}[/tex]