### Theory:

The distributive property states that multiplying a sum by a number gives the same result as multiplying each subtracted by the number and then subtracting the products together.
For any number $$a$$, $$b$$ and $$c$$, we have $$a × b - c = a × b - a × c$$.

Consider the number $$4$$, $$3$$ and $$2$$ we have

$$4 × 3 - 2 = 4 × 3 - 4 × 2$$. (LHS $$=$$ RHS)

LHS: $$4$$ $$×$$ $$2 - 3$$ $$=$$ $$4$$ $$×$$ $$1$$

$$=$$ $$4$$.

RHS: $$4$$ $$×$$ $$3$$ $$-$$ $$4$$ $$×$$ $$2$$

$$=$$ $$12$$ $$-$$ $$8$$

$$=$$ $$4$$.

Thus, $$4$$ $$×$$ $$3 - 2$$ $$=$$ $$4$$ $$×$$ $$3$$ $$-$$ $$4$$ $$×$$ $$2$$. (LHS $$=$$ RHS)

For any three rational numbers $\frac{a}{b}$, $\frac{c}{d}$ and $\frac{e}{f}$, we have $\frac{a}{b}$ $$×$$ $\left(\frac{c}{d}-\frac{e}{f}\right)$ $$=$$ $\left(\frac{a}{b}×\frac{c}{d}\right)$ $$-$$ $\left(\frac{a}{b}×\frac{e}{f}\right)$.

Consider the rational numbers $\frac{-3}{4}$$\frac{2}{3}$ and $\frac{-7}{6}$ we have

$\frac{-3}{4}$ $$×$$ $\left\{\frac{2}{3}-\frac{-7}{6}\right\}$  $$=$$ $\left(\frac{-3}{4}×\frac{2}{3}\right)$ $$-$$ $\left(\frac{-3}{4}×\frac{-7}{6}\right)$. (LHS $$=$$ RHS)

LHS: $\frac{-3}{4}$ $$×$$ $\left\{\frac{2}{3}-\frac{-7}{6}\right\}$

$\frac{-3}{4}$ $$×$$ $\left\{\frac{2}{3}-\frac{-7}{6}\right\}$ $$=$$ $\frac{-3}{4}$ $$×$$ $\left\{\frac{\left(4-\left(-7\right)\right)}{6}\right\}$

$$=$$ $\frac{-3}{4}$ $$×$$ $\frac{-11}{6}$ $$=$$ $\frac{33}{24}$.

RHS$\left(\frac{-3}{4}×\frac{2}{3}\right)$ $$-$$ $\left(\frac{-3}{4}×\frac{-7}{6}\right)$

$\left(\frac{-3}{4}×\frac{2}{3}\right)$ $$=$$ $\frac{-3×2}{4×3}$ $$=$$ $-\frac{6}{12}$ $$=$$ $-\frac{1}{2}$.

And $\left(\frac{-3}{4}×\frac{-7}{6}\right)$ $$=$$ $\frac{-21}{24}$.

Therefore $\left(\frac{-3}{4}×\frac{2}{3}\right)$ $$+$$ $\left(\frac{-3}{4}×\frac{-7}{6}\right)$ $$=$$ $-\frac{1}{2}$ $$-$$ $\frac{-21}{24}$ $$=$$ $\frac{33}{24}$.

Thus, $\frac{-3}{4}$ $$×$$ $\left\{\frac{2}{3}-\frac{-7}{6}\right\}$ $$=$$ $\left(\frac{-3}{4}×\frac{2}{3}\right)$ $$+$$ $\left(\frac{-3}{4}×\frac{-7}{6}\right)$. (LHS $$=$$ RHS)