CH3-OH + HBr ------> CH3Br + H2O
The next step requires a Gilman reagent, specifically (CH3)2Cu-Li+. Gilman reagents add chains to other molecules.
CH3BR + (CH3)2Cu-Li+ ------> CH3-CH3 + CH3BrCu+Li-
Treat the product with heat to deprotinate and produce ethene:
CH3-CH3 + heat -----> CH2=CH2
Treat the product with an acid and water:
CH2=CH2 + H2SO4 + H2O ------>CH3-CH2-OH