a,
(1) $2CH_4\xrightarrow{{1500^oC}} C_2H_2+3H_2$
(2) $C_2H_2+HCl\xrightarrow{{HgCl_2, t^o}} CH_2=CHCl$
(3) $nCH_2=CHCl\xrightarrow{{t^o, p, xt}} (\kern-6pt-CH_2-CHCl-\kern-6pt)_n$
b,
(1) $C_2H_2+H_2\xrightarrow{{Pd/PbCO_3, t^o}} C_2H_4$
(2) $nCH_2=CH_2\xrightarrow{{t^o, p, xt}} (\kern-6pt-CH_2-CH_2-\kern-6pt)_n$