The product of the ages of Adu and Tanko is 9 less than Akorfa's age. Tanko is 4 years older than Adu. Akorfa's age is six times Tanko's age. Find their ages.

Let $A$ be Adu's age.
Let $T$ be Tanko's age.
Let $K$ be Akorfa's age.

1. "The product of the ages of Adu and Tanko is 9 less than Akorfa's age."

2. "Tanko is 4 years older than Adu."

3. "Akorfa's age is six times Tanko's age."

From $(**)$, we can express $A$ as $A = T - 4$.
Substitute this into $(****)$:

Subtract $6T$ from both sides:

Add 9 to both sides:

We can factor the quadratic equation:

This gives two possible values for $T$:

If $T = 1$:
$1 = A + 4 \implies A = -3$. An age cannot be negative, so $T=1$ is not a valid solution.

If $T = 9$:
$9 = A + 4 \implies A = 5$. This is a valid age.

Using $T = 9$:

Akorfa's age is 54 years.

The final answer is $\text{54 years}$.