Mya has ballet lessons every sixth day and swimming every fourth day. today she has both lessons. in how many days will mya have both lessons on the same day again?

To determine when Mya will have both lessons again on the same day, you will list the multiples of each number of days because to show every 4 or 6 days, you will count by 4's and 6's.

When you get to the first number that is the same, that will be the next time she will have both lessons again.  This is called the least common multiple (LCM).

4, 8, 12, 16, 20, ...
6, 12, 18, 24

In 12 days she will have both lessons again.