1. The problem states: Solve for the unknown number $a$ in the equation $\frac{6}{8} = \frac{9}{a}$.\n\n2. We use the property of proportions: if $\frac{x}{y} = \frac{m}{n}$, then $x \times n = y \times m$.\n\n3. Applying this to our problem: $6 \times a = 8 \times 9$.\n\n4. Simplify the right side: $6a = 72$.\n\n5. To isolate $a$, divide both sides by 6: $a = \frac{72}{6}$.\n\n6. Simplify the fraction: $a = 12$.\n\nTherefore, the unknown number $a$ is 12.