Explanation

To solve this problem with examples, make a short list of possibilities for each of x and y:
x = 18, 36, 54…
y = 12, 24, 36…

Now try to disprove the statements by trying several combinations of x and y above. In the 1st statement, x + y could be 18 + 12 = 30, 54 + 12 = 66, 36 + 24 = 60, or many other combinations.

All of those combinations are multiples of 6. This makes sense, as x and y individually are multiples of 6, so their sum is, too. The first statement is true.

To test the second statement, xy could be 18(12) = 216, which is not divisible by 48. Eliminate the second statement.

As for the third statement, $\frac{x}{y}$ could be $\frac{18}{12}$, which is not even an integer (and therefore not divisible by 6), so the third statement is not necessarily true.