what is the value of x?

Answer:
A.[tex]\:\:2\sqrt{3} [/tex]
Step-by-step explanation:
By geometric mean theorem.
[tex]x = \sqrt{2 \times 6} \\ \\ \implies \: x = \sqrt{12} \\ \\ \implies \: x = \sqrt{ {(2)}^{2} \times 3} \\ \\ \implies \: x = 2\sqrt{3} [/tex]