Classify each listed unit operation by the mechanism it uses, and check whether that mechanism actually acts on organic carbon content. Let $X_{org}$ represent the organic matter fraction of sludge; a qualifying process should reduce $X_{org}$ substantially.
Digestion: mechanism is microbial metabolism, organic matter is consumed as a substrate by bacteria, so $X_{org}$ decreases via biological conversion to biogas or stabilized solids. Qualifies.
Incineration: mechanism is combustion at high temperature, organic matter is oxidized to $CO_2$ and $H_2O$, so $X_{org} \to 0$ essentially. Qualifies, giving close to complete removal.
Magnetic separation: mechanism is a magnetic field pulling out ferromagnetic particles, operating purely on a physical magnetic property of metallic objects, with zero interaction with the carbon based organic fraction of sludge, so $X_{org}$ is unaffected. Does not qualify.
Wet-oxidation: mechanism is liquid phase oxidation of dissolved and suspended organics under heat and pressure using an oxidant, so $X_{org}$ is again converted to $CO_2$, water, and simpler compounds. Qualifies.
Three of the four processes act directly on the organic fraction through biological, thermal, and oxidative mechanisms respectively, while magnetic separation acts on an unrelated physical property and is used for metal recovery, not organics removal.
\[\boxed{\text{Answer: (A) Digestion, (B) Incineration, (D) Wet-oxidation}}\]