A basketball player is 6 2/3 feet tall. His infant son is 1/4 as tall. How tall is his son?

To find how tall his son is, we need to multiply the father's height by 1/4: 6 2/3 feet * 1/4 = <<6+2/3*1/4=1 2/3>>1 2/3 feet. Answer: \boxed{1\frac{2}{3}}.

To find out how tall the basketball player's son is, we need to multiply his height by the given fraction.

The basketball player's height is 6 2/3 feet, which can be expressed as a mixed fraction: 6 + 2/3 = 18/3 + 2/3 = 20/3 feet.

Now, to find the son's height, we multiply the player's height by 1/4:

(20/3) * (1/4) = (20*1) / (3*4) = 20/12 = 5/3 feet.

Therefore, the son is 5/3 feet tall.