Will The Boeing 747-8F And 777F Compete

Uh?

Unlikely.
Besides, they're transport aircraft so there is not that much ''competition''
the freight airline just chooses which aircraft suites best their needs.
747 has bigger cargo capacity & range, & 777 is slightly more efficient, & perhaps cheaper to operate but with less cargo capacity & slightly less range.
furthermore, 747-8F & 777F r both from Boeing so either way, its cash for Boeing.


l am assuming u meant the 747 & the 777 competing against each other.

If u meant the 747 or 777 competing against existing freight aircraft market, then l would say that it would work but it wo not bring a fortune for Boeing.
existing aircraft, 747s or 777s etc can easily be converted to freight aircraft. It is also obviously cheaper than buying brand new aircraft too.

they're both boeing so they wont make 2 products which compete with eachother dude.

No they won't, the 747-8F will be for freight carriers who want to transport denser cargo over a shorter range.

they really are suited for different missions. two engines will always be more efficient tha four, so the 747 is only preferred where the 777 does not have the lift or the legs

They fit into different sectors. You want a huge amount of payload delivered to Hubs, go 747. You have a lesser amount that is economical delivered point to point, 777. Same thing applies to the general airframe whether it is cargo or passengers. That is the root of controversy between the 787 and 380. Only the future will tell which strategy is superior.