Dear Ashim, there are numerous methods to convert methanol to ethanol. Here are some of them -

• CH3OH (methanol) + red P/I2 or, HI ---->CH3I (methyl iodide) + KCN ----->CH3CN(methyl cyanide) +Na/C2H5OH ------>CH3CH2NH2 +HNO2 ------->CH3CH2OH (ethanol)
• firstly convert methanol to methyl alcohol in presence of PI3 and then to methyl magnesium iodide in presence of mg/ether and then apply grignard reaction
•  CH3OH+HCl----->CH3Cl 2CH3Cl+2Na------->CH3-CH3+2NaCl(DryEther)CH3-CH3+HCl----->CH3-CH2-Cl+H2CH3-CH2-Cl+KOH(aq)----->CH3-CH2-OH

All the best 

Hope this helps 

Hey Ashim, the procedure is as follows:

STEP 1 : Converting methyl alcohol to chloromethane

When methyl alcohol reacts with hydrogen chloride, it leads to substitution of alcoholic group and results in the formation of chloromethane.

CH₃OH + HCI→ CH₃Cl

STEP 2: Converting chloromethane to ethanenitrile.

When chloromethane is reacted with aqueous alcoholic solution of KCN, it results in the formation of ethanenitrile.

CH₃Cl + KCN →CH₃CN + KCI

STEP 3: Converting ethanenitrile to ethanoic acid.

When hydrolysis of ethaninitrile in hot acidic or alkaline medium is carried out, it leads to the formation of ethanoic acid.

CH₃CN  + ( Hydrolysis H₃O⁺) → CH₃COOH

STEP 4: Converting ethanoic acid to ethyl alcohol.

When reduction of ethanoic acid is carried out i the presence of strong reducing agent such as , it leads to the formation of ethyl alcohol or ethanol.

CH₃COOH⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻ (LiAlH₄) → CH₃CH₂OH

Hope it helps, good luck!