In this pattern, multiply by 4 and then multiply by 1/2. This repeats every time.
Therefore, the next numbers in the patter would be 96 and 48.
In order to find this, you can always divide each number by the number that comes prior to it. below are the examples.
12/3 = 4
6/12 = 1/2
24/6 = 4
12/24 = 1/2
48/12 = 4
24/48 = 1/2
Once we see this repeat, we know that this must be the pattern.