f ( x ) = ( x + 6 ) ( x + 5 ) (

Choice B is correct. It’s given that $f\left(x\right)=(x+6)(x+5)(x-4)$ and $y=f\left(x\right)-3$. Substituting $(x+6)(x+5)(x-4)$ for $f\left(x\right)$ in the equation $y=f\left(x\right)-3$ yields $y=(x+6)(x+5)(x-4)-3$. Substituting $-6$ for $x$ in this equation yields $y=(-6+6)(-6+5)(-6-4)-3$, or $y=-3$. Substituting $-5$ for $x$ in the equation $y=(x+6)(x+5)(x-4)-3$ yields $y=(-5+6)(-5+5)(-5-4)-3$, or $y=-3$. Substituting $4$ for $x$ in the equation $y=(x+6)(x+5)(x-4)-3$ yields $y=(4+6)(4+5)(4-4)-3$, or $y=-3$. Therefore, when $x=-6$ then $y=-3$, when $x=-5$ then $y=-3$, and when $x=4$ then $y=-3$. Thus, the table of values in choice B represents $y=f\left(x\right)-3$.

Choice A is incorrect. This table represents $y=x-3$ rather than $y=f\left(x\right)-3$.

Choice C is incorrect. This table represents $y=x+3$ rather than $y=f\left(x\right)-3$.

Choice D is incorrect. This table represents $y=f\left(x\right)+3$ rather than $y=f\left(x\right)-3$.