Explanation

[Solution by Dr. Abubacker] The cation is allylic; the substituent on the far end of the allyl system decides stability. In option (2) the oxygen lone pair of $-OCH_3$ is directly conjugated with the allyl cation (+M effect), giving an extra oxocarbenium resonance form. In (4) the acetyl group withdraws the oxygen lone pair, in (3) $F$ is a weaker donor, and in (1) the $-CH_2OCH_3$ group is only inductively withdrawing. So (2) is the most stable. Answer (2).