To solve for the greatest possible value of \(P\), we resolve the forces parallel and perpendicular to the plane.

1. Resolve forces perpendicular to the plane:

\(12g \cos 25 = R + P \sin 8\)

2. Resolve forces parallel to the plane:

\(P \cos 8 = F + 12g \sin 25\)

3. The frictional force \(F\) is given by:

\(F = 0.3R\)

4. Substitute \(F = 0.3R\) into the parallel force equation:

\(P \cos 8 = 0.3R + 12g \sin 25\)

5. Substitute \(R = 12g \cos 25 - P \sin 8\) from the perpendicular equation into the parallel equation:

\(P \cos 8 = 0.3(12g \cos 25 - P \sin 8) + 12g \sin 25\)

6. Solve for \(P\):

\(P = 80.8\)