The other tutor assumed you have studied the law of cosines.
I am guessing that you haven't. I think you've only had the
Pythagorean theorem.  Maybe you haven't even gotten to
trigonometry.  Am I right? If so then do it this way:

The angles of the triangle are 30°-30°-120°. Two of the sides lengths are 2
times the square root of 3. What is the length of the third side?



The triangle is isosceles because two sides and two angles have the
same measure.  So draw a perpendicular to the base, which also
bisects both the third side as well as the 120° vertex angle. like this:



It bisects the 120° into two 60° angles like this:



Let each of the two halves of the third side be x:



Now for the right triangle on the left:



Since this is a 30°-60°-90° right triangle, we know that
the shorter leg (the green side) is one-half of the hypotenuse.
So we can label it one-half of  , which is 
, like this:


 
 Now we can use the Pythagorean theorem to find the longer leg:

















And so the right triangle has longer leg of 3



Now we put the original triangle back together like this:



And we end up with



Edwin