Let the common difference of the arithmetic progression be \(d\). Then, the 4th term is \(a + 3d = -6\), where \(a\) is the first term. Also, the sum of the 8th and 9th terms is \((a + 7d) + (a + 8d) = 2a + 15d = 72\).

We have the system of equations:

\(a + 3d = -6\).

\(2a + 15d = 72\).

Solve this system of equations to find \(d\):

Multiply the first equation by \(2\) and subtract it from the second equation:

\(2a + 15d - 2(a + 3d) = 72 - 2(-6)\).

\(2a + 15d - 2a - 6d = 84\).

\(9d = 84\).

\(d = 9\frac{1}{3}\).

Therefore, the common difference is \(9\frac{1}{3}\).