Question

how will you convert methane into propyne ?​

Answer 1

Methane being as unreactive as any alkane to most reactions (having a pKa of about 50~60), we pretty much have to begin with a radicalhalogenation to turn it into a reactive species. Specifically we can go with radical brominationbecause for experimental reasons it gives a better yield than radical chlorination.

From that point, we can get a bit more... original/creative.

MAKING PROPANE

Making propane is not extremely difficult from here; simply use a very strong lewis base like sodium hydride or sodium amide to deprotonateacetylene.

Then you can react that as a nucleophile with the alkyl halide (as an electrophile) you just made to generate methylacetylene, which reduces down to the alkane via H2 catalyzed by Pd over C