The given equation is \((K2)_6 \cdot 3_6 = 3_5 \cdot (K4)_5\).

Let's first convert the numbers to their decimal equivalents:

\((K2)_6 = 6k + 2\)

\(3_6 = 3\)

\(3_5 = 3\)

\((K4)_5 = 5k + 4\)

Now, we can rewrite the equation using decimal values:

\((6k + 2) \cdot 3 = 3 \cdot (5k + 4)\)

Simplify the equation:

\(18k + 6 = 15k + 12\)

Subtract \(15k\) from both sides:

\(3k + 6 = 12\)

Subtract 6 from both sides:

\(3k = 6\)

Finally, divide by 3:

\(k = 2\)