fuji hakone day pass

there are 2 prices for the day pass
8,000 ~ 5,600
if I were to depart from Shinjuku station can I
use 5,600 pass, also I will be staying in Fuji, Hakone for four days
what would you surgest?

You can't use 5600 pass if you depart from Shinjuku station.
8000 pass is good.

No. The pass costs 8,000 yen and includes round-trip travel from Tokyo (Shinjuku) if purchased at Shinjuku Station. It costs 5,600 yen at Odawara Station, however this does not include any travel to/from Tokyo. More information is here: http://www.japan-guide.com/e/e2358_014.html