Being $4$ degrees from $18$ means the distance between $t$ and $18$ on the number line is $4$. Absolute value represents distance, so the correct equation is $|t-18|=4$.

For an equation of the form $|x-4|=7$, the expression inside the absolute value can be either $7$ or $-7$. So $x-4=7$ gives $x=11$, and $x-4=-7$ gives $x=-3$. Since the question asks for one possible value, $-3$ is a correct answer.

By definition, an absolute value represents distance from $0$ on the number line. So $|x-4|$ represents the distance between $x$ and $4$. That description is equivalent for every value of $x$.

Because the point is on $y=|x+2|$ and has $y=5$, it must satisfy $|x+2|=5$. This means the distance from $x$ to $-2$ is $5$, so $x$ could be $-7$ or $3$. Among the choices, only $(-7,5)$ has $y=5$ and matches the equation. Therefore, $(-7,5)$ is the correct coordinate.

From the system, $|p+2|=6$. That means $p+2=6$ or $p+2=-6$, so $p=4$ or $p=-8$. Since the question says $p$ is to the right of $-2$, the value must be greater than $-2$. Therefore, $p=4$.