The Rams play the NFC East every three years (2017, 2020, 2023, etc.). In 2020 the teams they play at home this year (Was & Phi) will be away games and the teams they travel to this year (NYG & Dal) will be home games. So to answer your question: 2020 ... with a disclaimer. In 2018 & 2019 the Rams will play the team from the NFC East that finishes the same spot as the Rams. If the Rams and Giants both finish first (or both finish 2nd, etc.) they will play each other then, too. Whether that is home or away will depend on where they finish in their division. (The 1st and 3rd place teams will play @ the team from one division, the 2nd and 4th place teams will play @ the team from the other division. Too tired to look up which one is East and which one is West :-) )
The Rams also play the AFC East every 4 years. They played them last year so they will also play them again in 2020. The Jets and Patriots will travel to LA then and the Rams will play at BUF and MIA.
AlbaNY_Ram
