To figure out how likely it is to have 4 out of 4 people, you calculate
.5 x .5 x .5 x.5 = 0.0625
That assumes independent events that really occur half the time (.5)
However, about 90% of people are right handed so the probability of a left black eye is much higher than .5
I should have added - we really don’t know if it is 4 out of 4 people or 8 out of 8 people. It could be, for example, 4 out of 6 or 8 out of 12. We aren’t shown those who had a black eye on the right side.