ΔABC and ΔCBD are similar. Therefore we have the proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\\\AB=6;\ BC=x;\ BD=2[/tex]
Substitute:
[tex]\dfrac{6}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex](x)(x)=(6)(2)\\\\x^2=12\to x=\sqrt{12}\\\\x=\sqrt{4\cdot3}\\\\x=\sqrt4\cdot\sqrt3\\\\\boxed{x=2\sqrt3}[/tex]
