It will be very hard for westham to finish in the fourth position because the team ahead of them(Tottenham, arsenal and Manchester United) have a better squad than them and more depth than them
Even I doubt if Westham can finish in 6th place at the end of the season. Westham performance looks decreasing gradually, sadly they must play with strong teams in the last few matches. After they got some draws playing against Leicester City and Newcastle, they got 0 points in 2 next matches. It is the reason why their position dropped so much to 7th place.