The function g is defined by g ( x ) = | x + 18 |

Choice D is correct. The value of $g\left(4\right)$ is the value of $g\left(x\right)$ when $x=4$. Substituting $4$ for $x$ in the given equation yields $g\left(4\right)=\left.4+18\right|$, which is equivalent to $g\left(4\right)=\left.22\right|$, or $g\left(4\right)=22$. Therefore, the value of $g\left(4\right)$ is $22$.

Choice A is incorrect. This would be the value of $g\left(4\right)$ if function $g$ was defined by $g\left(x\right)=-\left.18\right|$, not $g\left(x\right)=\left.x+18\right|$.

Choice B is incorrect. This would be the value of $g\left(4\right)$ if function $g$ was defined by $g\left(x\right)=-\left.x\right|$, not $g\left(x\right)=\left.x+18\right|$.

Choice C is incorrect. This would be the value of $g\left(4\right)$ if function $g$ was defined by $g\left(x\right)=\left.-x+18\right|$, not $g\left(x\right)=\left.x+18\right|$.