First, simplify the right side of the equation.

log6(24-9) can be calculated to equal log6(15), so the equation becomes:

log6 (2x + 3) = log6 (15) - 1

Next, use the properties of logarithms to rewrite the equation:

log6 (2x + 3) = log6 (15/6)

Now, set the expressions inside the logarithms equal to each other:

2x + 3 = 15/6

Simplify the right side of the equation:

2x + 3 = 2.5

Subtract 3 from both sides:

2x = -0.5

Divide by 2 on both sides to solve for x:

x = -0.25

Therefore the solution to the equation log6 (2x + 3) = log6 (15) - 1 is x = -0.25.