First of all, we find all our multiples of 4 & 6, then stop when the multiples are 60 or above 60.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
As you can see, we have 5 common multiples.
So, they will blink 5 times at the same time.