In the XY-coordinate plane, point P is a distance of $4$ from the point $(1, 1)$. Which of the following could be P?

It may help a lot to make a figure so you can visualize what is going on:

The figure above shows the point $(1, 1)$ along with the five possible answers for point P.

Only answer B, point $(1, 5)$, is a distance of $4$ from point $(1, 1)$: the y value increases by $4$ units to go from $(1, 1)$ to $(1, 5)$, and the x-value doesn't change.