The least common multiple means that you need to find the least common number that both numbers can be multiplied to. Whenever you multiply them by each other, you will get an answer, but it won't necessarily be the "least" common number they can be raised to. You can divide that number by 2, and you will get the answer. In this case, 6 x 8= 48; divide it by 2, and the answer, 24, is correct.
You can try to understand the problem by applying common sense. Start by raising your largest number to multiples of it. An 8 can be multiplied by 2 to get a 16, but a 6 can't be raised to 16. Try 8 x 3. That's a 24, and your 6 can be raised to a 24 (4 x 6 =24), so 24 is the LCM.
You have:
6, 12, 18, 24
8, 16, 24
Yes, it is 24
So that's the method I used to get the least common multiple of 8 and 6.