What is the Least common Denominator (LCD) of 7/8 and 1/6?

24.
Since you’re only looking for the denominator, you can ignore the numerators for now and focus and the 8 and the 6.
This works just like LCM (least common multiple): find the first number in common when you count up the lists of multiples for each.
There isn’t a number easy to pick from here such as 5 or 10, so you’ll have to go up both lists. The first five values is reasonable:
6, 12, 18, 24, 30
8, 16, 24, 32, 40
24 is the first common number between the two lists, so there’s your common denominator.