Let's go through the answer choices to see which relation is a function or not.
A) We don't have a function because x = 10 repeats itself. We see that x = 10 leads to y = 5 and y = 15 at the same time. We cannot have an x input lead to multiple outputs.
B) The list of x coordinates of the points is: 8, 4, 12, 16, 20. None of the x values repeat, so we have a function. Choice B is the answer. If you plot the four points on the same xy grid, then you'll see the graph passes the vertical line test. Any given input x leads to exactly one output y.
C) We have x = 4 repeated, so we don't have a function. The two points (4,8) and (4,12) are on the same vertical line, which is why this graph fails the vertical line test. The input x = 4 leads to the simultaneous outputs of y = 8 and y = 12, which is not valid for a function.
D) The input x = 2 leads to the outputs y = 6 and y = 7, so we can cross this off the list. The ordered pairs for this diagram are (1,5), (2,6), (2,7), (3,8) and (4,8). The points (2,6) and (2,7) have the same x coordinate. It is possible to repeat the y coordinate and still have a function. All we worry about is the repeated x values.
