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\frac{4\sqrt{3}}{\sqrt{64}}\times \frac{2}{\sqrt{3}}
Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.
\frac{4\sqrt{3}}{8}\times \frac{2}{\sqrt{3}}
Calculate the square root of 64 and get 8.
\frac{1}{2}\sqrt{3}\times \frac{2}{\sqrt{3}}
Divide 4\sqrt{3} by 8 to get \frac{1}{2}\sqrt{3}.
\frac{1}{2}\sqrt{3}\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{1}{2}\sqrt{3}\times \frac{2\sqrt{3}}{3}
The square of \sqrt{3} is 3.
\frac{2\sqrt{3}}{2\times 3}\sqrt{3}
Multiply \frac{1}{2} times \frac{2\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{\sqrt{3}}{3}\sqrt{3}
Cancel out 2 in both numerator and denominator.
\frac{\sqrt{3}\sqrt{3}}{3}
Express \frac{\sqrt{3}}{3}\sqrt{3} as a single fraction.
\frac{3}{3}
Multiply \sqrt{3} and \sqrt{3} to get 3.
1
Divide 3 by 3 to get 1.