Simplify: 2(√4/6 ÷2√3/5)

$$\sqrt{4} = 2$$

Substitute this value back into the expression:

$$2\left(\frac{2}{6} \div \frac{2\sqrt{3}}{5}\right)$$

$$\frac{2}{6} = \frac{1}{3}$$

The expression becomes:

$$2\left(\frac{1}{3} \div \frac{2\sqrt{3}}{5}\right)$$

To divide by a fraction, multiply by its reciprocal.

$$\frac{1}{3} \div \frac{2\sqrt{3}}{5} = \frac{1}{3} \times \frac{5}{2\sqrt{3}} = \frac{5}{6\sqrt{3}}$$

The expression is now:

$$2\left(\frac{5}{6\sqrt{3}}\right)$$

$$\frac{5}{3\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{5\sqrt{3}}{3 \times (\sqrt{3})^2} = \frac{5\sqrt{3}}{3 \times 3} = \frac{5\sqrt{3}}{9}$$

The simplified expression is $\frac{5\sqrt{3}}{9}$.