The vertical lines are "absolute value" indicators. The Absolute Value operation strips away any negative signs from the numbers inside, so that only the positive distance from zero is retained.
-15 is less than 9 because -15 is farther left on the number line than is 9.
However, |-15| is 15, and |9| is 9; therefore, |-15| lies to the right of |9| on the number line, which means it is greater.
Only the first of your two statements is true.
