check the picture below.
[tex]\bf 8\sqrt{6}=a\sqrt{2}\implies \cfrac{8\sqrt{6}}{\sqrt{2}}=a\implies \stackrel{rationalizing~it}{\cfrac{8\sqrt{6}}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}}=a\implies \cfrac{8\sqrt{12}}{2}=a
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4\sqrt{12}=a\implies 4\sqrt{2^2\cdot 3}=a\implies \boxed{8\sqrt{3}=a}\\\\
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[tex]\bf 2b=a\implies b=\cfrac{a}{2}\implies b=\cfrac{8\sqrt{3}}{2}\implies \boxed{b=4\sqrt{3}}\\\\
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x=b\sqrt{3}\implies x=4\sqrt{3}\cdot \sqrt{3}\implies x=4\sqrt{3^2}\implies \boxed{x=12}[/tex]
