g x = 3 5 x + 7 6 h x = 6 x - 5

Choice D is correct. It’s given that $g\left(x\right)=\frac{3}{5}x+\frac{7}{6}$ and $h\left(x\right)=6x-5$. Substituting $\frac{3}{5}x+\frac{7}{6}$ for $g\left(x\right)$ and $6x-5$ for $h\left(x\right)$ in the expression $g\left(x\right)·h\left(x\right)$ yields $\left(\frac{3}{5}x+\frac{7}{6}\right)\left(6x-5\right)$. This expression can be rewritten as $\frac{3}{5}x\left(6x-5\right)+\frac{7}{6}\left(6x-5\right)$, or $\frac{18x^2}{5}-3x+7x-\frac{35}{6}$, which is equivalent to $\frac{18x^2}{5}+4x-\frac{35}{6}$.

Choice A is incorrect. This expression is equivalent to $\frac{3}{5}x\left(6x\right)+\frac{7}{6}\left(-5\right)$, not $\left(\frac{3}{5}x+\frac{7}{6}\right)\left(6x-5\right)$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This expression is equivalent to $\left(\frac{3}{5}x-\frac{7}{6}\right)\left(6x+5\right)$, not $\left(\frac{3}{5}x+\frac{7}{6}\right)\left(6x-5\right)$.