To understand why a methyl group stabilizes a carbocation, we need to delve into the concept of hyperconjugation. A carbocation is an organic ion in which a carbon atom has three bonds and a positive charge, and it's typically quite unstable due to the electron deficiency.
The presence of a methyl group adjacent to the positively charged carbon can help stabilize the carbocation through hyperconjugation. This effect involves the delocalization of electrons from the C-H sigma bonds in the methyl group into the empty p-orbital of the carbocation, thereby distributing the positive charge over a larger volume, which stabilizes the ion.
Here's why the other options are not applicable:
In conclusion, among the provided options, hyperconjugation is the primary stabilizing effect for carbocations with adjacent alkyl groups like methyl. The methyl group provides electron density through hyperconjugation, which helps in dispersing the positive charge across the molecular structure, thus stabilizing the carbocation.

Identify the suitable reagent for the following conversion: $Ph-C(=O)-OCH_3$ $\longrightarrow$ $Ph-CHO$