The least common multiple of a number "n" and 6 is 24. What is the value for "n"?

Let's consider the prime factorization of both given numbers, 6 and 24.
It is clear that 6 = 2^1 * 3^1  and  24 = 2^3 * 3^1.
Hence the number n must contain 2 exactly in degree 3 in its prime factorization. If it would have 2 in greater degree, the LCM of 6 and n would have 2 in that greater degree, and if in less, then in less.
Also n may contain 3 in degree not greater than 1. It may contain 3 in degrees 0 or 1, because 6 already have 3^1 and 24 also.
And it cannot have any other prime factors.
This gives us two options for n:  2^3 * 3^0 = 8 and 2^3 * 3^1 = 24.