What is the value of x?

[tex]\text{In}~ \triangle ABC,\\\\~~~~~~~~\sin 45^{\circ} =\dfrac{BC}{AC} \\\\\implies \dfrac 1{\sqrt 2} = \dfrac{BC}{6\sqrt 2}\\\\\\ \implies BC= 6\\\\\text{Now, In}~ \triangle BCD\\\\~~~~~~\cos 60^{\circ} = \dfrac{BD}{BC}\\\\\ \implies \dfrac 12 = \dfrac{x}{6}\\\\\\\implies x = \dfrac 62\\\\\\\implies x = 3[/tex]