Work out 3/7 * 16/9 and answer in its simplest form.

Step 1: Write the given expression.

$\frac{7}{9} \times 3 \times \frac{16}{7}$

Step 2: Cancel the common factor of 7 in the numerator and denominator.

$\frac{7}{9} \times 3 \times \frac{16}{7} = \frac{1}{9} \times 3 \times 16$

Step 3: Rewrite as a single fraction.

$\frac{3 \times 16}{9}$

Step 4: Multiply the numerator.

$3 \times 16 = 48$

$\frac{48}{9}$

Step 5: Simplify by dividing numerator and denominator by 3.

$48 \div 3 = 16$

$9 \div 3 = 3$

$\frac{16}{3}$

$\boxed{\dfrac{16}{3}}$