The ratio of black to red is 3 to 5, so it's sort of like you have sets of 3+5 = 8 checkers.
If you have 16 checkers then you have 16/8 = 2 sets.
2 sets would have 2*3 = 6 black checkers.
2 sets would have 2*5 = 10 red checkers.
Answer: 6 black checkers.