given some input (from the domain) to a function, the function must return exactly one output (in the range)

Since your table has one value (8) returning 2 values (4 & 6) that table can't be describing a function.

The answer is simply applying the definition of a function.

maybe it would help you to think of it in normal "function" syntax rather than as a table.

f(4) = 2

f(12) = 3

but

f(8) =6

f(8)=4

therefore f is not a function, because a function can't return 2 answers for one input.