You could use pythagorean theorem to solve the problem. Look at one of the right triangle on the picture, either the right one or the left one.
Pythagorean Theorem: The sum of the squares of the perpendicular sides is equal to the square of hypotenuse.
a² + (2√3)² = (4√3)²
a² + (2√3)(2√3) = (4√3)(4√3)
a² + (4 × 3) = (16 × 3)
a² + 12 = 48
a² = 48 - 12
a² = 36
a = √36
a = 6
The altitute is 6 units