In a right triangle, the sum of the squares of the legs is the square of the hypotenuse.
So, you would have
[tex] a^2+b^2=c^2 [/tex]
If you plug the values, you have
[tex] (2\sqrt{3})^2+b^2=(2b)^2 [/tex]
So, you end up with a quadric equation in b:
[tex] 12+b^2=4b^2 \iff 3b^2=12 \iff b^2=4 \iff b=2 [/tex]
So, the three sides are
[tex] a=2\sqrt{3},\ b=2,\ c=4 [/tex]
