I am not entirely sure if it would be difficult. 4k is about 2.5x or so away from the current price, which means that it could happen in 3 months give or take. We are not in a bull run right now, but when the market goes into bull run that means it could technically be a lot better.
That is the case.. "we are not in a bull run right now" meaning ETH is still in the bear market, this hype and price recovery is just an effect of an artificial hype created by the merge event. If ETH failed to hit $4k during this upcoming event, I do not think $4k is possible for ETH this 2022. There are some possibilities but it is kinda slim. Like hype continuing after the merge and eventually creating FOMO. If that happens, even $5k is possible. But if not, I think we will be back again at $1k - $1.5k ETH a piece.
I hope for it to be much better in the long run, 4k could be achieved, or maybe it won't be but gets closed but another big increase should happen. We dropped from 64k to under 30k in 2021 and then in October went to 68k again from there, so there is no way of knowing if it will be all the way up again or not, if that happens then 4k is not that impossible at all.
Sorry, this is kinda confusing, it seems you had missed an identifier in this statement and somehow mixed your statement on ETH and BTC.