Let's evaluate each reaction type and match them accordingly:
P. Methylcyclohexane $\rightarrow$ Toluene + 3H$_2$
This is a dehydrocyclization reaction, where a cyclohexane ring is converted into a benzene ring with the release of hydrogen. Hence, P matches with III. Dehydrogenation.
Q. Ethylcyclopentane $\rightarrow$ Methylcyclohexane
This is an isomerization reaction, where the structure of the molecule is rearranged to form a different isomer. Hence, Q matches with IV. Isomerization.
R. n-Octane $\rightarrow$ Ethylbenzene + 4H$_2$
This reaction involves the removal of hydrogen atoms, which is typical of dehydrogenation reactions. Hence, R matches with I. Dehydrocyclization.
S. n-Octane $\rightarrow$ n-Pentane + Propylene
This is a cracking reaction, where a large molecule is broken down into smaller molecules. Hence, S matches with II. Cracking.
Thus, the correct combination is P – III, Q – IV, R – I, S – II.