When you need to find a common denominator for two or more fractions, the first thing you need to do is find the least common multiple of all the denominators which is called the LCM. The LCM will be your smallest common denominator.
You have to add the fractions 3/12 and 7/8 in this problem. So first find the LCM of 12 and 8. There are a several ways to do this. If you know how to split the numbers 8 and 12 into prime factors there is an easy way to find it, or alternatively you can just look at the multiples of 8 and 12
multiples of 8 are 8, 16, 24, 32..
multiples of 12 are 12, 24, 36,..
We see that 24 is the lowest number that is a multiple of both 12 and 8 (it's called the LCM of 12 and 8) so we can use 24 as a common denominator for the two fractions. This method works with adding 3 or 4 fractions also.
So 3/12 = 6/24 by multiplying the numerator and denominator by 2.
And 7/8 = 21/24 by multiplying the numerator and denominator by 3.
3/12 + 7/8 = 6/24 + 21/24 = 27/24