The formal definition of a function states that: "A function relates each element of a set with exactly one element of another set (possibly the same set)."
The part "..with exactly one element.." means that for every input (x-coordinate), it cannot give back 2 or more return values (y-coordinates). With that rule alone, we can look at the different groups of coordinate points, and find which of the groups don't have repeating x-coordinates.
Let us look at each group:
{(-6, 4), (-6, 2), (2, 9), (1, 4)} contains 2 pairs with the -6 x-coordinate, so this is not a function.
{(1, 2), (4, -1), (1, 2), (-3, 4)} contains 2 pairs with the 1 x-coordinate so this is not a function.
{(8, -2), (-4, 3), (8, 4), (-2, 3)} contains 2 pairs with the 8 x-coordinate so this is not a function.
{(8, 2), (9, -2), (7, 0), (-3, 6)} does not have any repeating x-coordinates, so this relation is a function.