Two sides of the triangle are 6 and 6 square root 3.

So the third side 6 or 6 square root 3

1) One of the angles of the triangle is obtuse.

One angle is obtuse and the two other angles are acute. Sides opposite to the acute angles are equal and smaller than the third side. Therefore the third side is 6.

2) The perimeter of the triangle is less than 24.

Let the third side be 6 square root 3

Therefore, perimter = 6 + 6 square root 3 + 6 square root 3 = apprx 27

But the perimeter is less than 24. Therefore the third side has to be 6.

Therefore perimter = 6 +6 +6 square root 3 = apprx 22.4.

Answer = D