$$8x^{3}+43x^{2}-30x-\left(9x+2\right)\left(4x^{2}-3x\right)$$
Use the distributive property to multiply $9x+2$ by $4x^{2}-3x$ and combine like terms.$$8x^{3}+43x^{2}-30x-\left(36x^{3}-19x^{2}-6x\right)$$
To find the opposite of $36x^{3}-19x^{2}-6x$, find the opposite of each term.$$8x^{3}+43x^{2}-30x-36x^{3}+19x^{2}+6x$$
Combine $8x^{3}$ and $-36x^{3}$ to get $-28x^{3}$.$$-28x^{3}+43x^{2}-30x+19x^{2}+6x$$
Combine $43x^{2}$ and $19x^{2}$ to get $62x^{2}$.$$-28x^{3}+62x^{2}-30x+6x$$
Combine $-30x$ and $6x$ to get $-24x$.$$-28x^{3}+62x^{2}-24x$$