$$\frac { n } { 2 } - \frac { 3 h } { 4 } + \frac { 5 n } { 6 } = 2$$
$h=\frac{16n}{9}-\frac{8}{3}$
$$6n-3\times 3h+2\times 5n=24$$
$$6n-9h+2\times 5n=24$$
$$6n-9h+10n=24$$
$$16n-9h=24$$
$$-9h=24-16n$$
$$\frac{-9h}{-9}=\frac{24-16n}{-9}$$
$$h=\frac{24-16n}{-9}$$
$$h=\frac{16n}{9}-\frac{8}{3}$$
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$n=\frac{9h}{16}+\frac{3}{2}$
$$16n=24+9h$$
$$16n=9h+24$$
$$\frac{16n}{16}=\frac{9h+24}{16}$$
$$n=\frac{9h+24}{16}$$
$$n=\frac{9h}{16}+\frac{3}{2}$$