Question

Convert Ethane to methane

Answer 1

ETHANE ON CHLORINATION GIVES CHLOROETHANE ON REACTION WITH AQ.KOH GIVES ALCOHOL ON OXIDATION FORMS ACETIC ACID ON REACTION WITH NaOH GIVES SODIUM FORMATE FINALLY THIS ON REACTION WITH SODALIME  GIVES METHANE

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Answer 2

EtH+Br2=EtBr+HBr (Free Radical halogenation, sunlight)
EtBr+NaOEt=C2H4+NaBr+EtOH (1,2 Elimination)
C2H4------> 2HCHO (Ozonolysis)
HCHO------>MeH (methane)- Clemmensen reduction by Zn/HCl
You can also reduce formaldehyde to methanol by NaBH4, halogenate with PX3 and reduce again with Bu3SnH

If you are ready to sacrifice 1 carbon.
EtBr----->EtOH (aqueous base)
EtOH----->AcONa (basic NaMnO4)
AcONa------> MeH+ Na2CO3 (sodalime decarboxylation)

Butane can be taken down to acetaldehyde in a similar fashion. Reduce that to ethanol, then ethyl bromide and place it back in the cycle.

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