The most stable carbocation from the following is :

Carbocation stability is governed mainly by two effects: (i) resonance delocalisation of the positive charge and (ii) hyperconjugation/inductive donation from adjacent $$C-H$$ or $$C-C$$ bonds. When both effects are possible, resonance is much more powerful than hyperconjugation.

Step 1 - Write the skeletal formulae of the four given carbocations.
Option A : $$\left(CH_3\right)_3C^{+}$$ (tert-butyl, a simple 3° alkyl carbocation)
Option B : $$C_6H_5CH_2^{+}$$ (benzyl carbocation)
Option C : $$(C_6H_5)_3C^{+}$$ (triphenylmethyl carbocation)
Option D : $$CH_2\;=\;CH\;CH_2^{+}$$ (allyl carbocation)

Step 2 - Analyse resonance possibilities.
• Option A has no resonance. Charge is localised on one carbon.
• Option D is an allylic cation; the positive charge delocalises over two carbons through one $$C=C$$ bond giving 2 major resonance forms.
• Option B is benzylic; the charge can resonate into the aromatic ring, producing 5 additional Kekulé structures (total 6).
• Option C is triphenylmethyl; the charge can be delocalised independently into each of the three phenyl rings. Each ring contributes 5 extra structures, so there are $$1 + 3 \times 5 = 16$$ significant resonance contributors. Thus the positive charge is spread over a very large π-system.

Step 3 - Consider hyperconjugation and inductive effects.
• Option A possesses nine β-hydrogens, giving nine hyperconjugative structures, but lacks resonance.
• Options B and D have only two β-hydrogens each, so hyperconjugation is much weaker than in Option A; however their resonance makes them more stable than A.
• Option C, besides enormous resonance, still has three benzylic β-hydrogens; hyperconjugation adds a small extra stabilisation.

Step 4 - Rank the overall stability.
Because resonance >> hyperconjugation, the order is
$$\text{triphenylmethyl} \; \gt \; \text{benzyl} \; \gt \; \text{allyl} \; \gt \; \text{tert-butyl}$$

Hence the most stable carbocation among the four is the triphenylmethyl carbocation.

Option C which is: triphenylmethyl carbocation