If Acceptable Losses is played and I have to kill Forge of the Future, does it effect take place?

No, the effect of Forge of the Future does not take place if it is killed by Acceptable Losses.

Here is the breakdown of why:

1. Activated Ability vs. Passive Effect: According to the card text and RiftJudge FAQs, the ability on Forge of the Future ("Kill this: Recycle up to 4 cards...") is an activated ability. The text "Kill this:" before the colon indicates that killing the card is a cost you must pay to activate the ability.
2. Acceptable Losses: When you are forced to kill a gear by Acceptable Losses, you are fulfilling the requirement of the spell's effect. You are not "activating" the Forge of the Future's ability; you are simply destroying it as a result of the spell's resolution.
3. No Activation: Because you did not choose to pay the cost to activate the Forge of the Future's ability, the ability never goes on the chain and does not resolve.

According to RiftJudge FAQ #5382:

"'Kill This' is an activated ability where killing the card is the cost to activate the ability, as indicated by the colon (':') in the card text. ... This is an activated ability, not a passive effect that can be used at any time without structure."

Since Acceptable Losses is forcing the destruction of the card rather than you paying the cost to activate it, the recycle effect does not trigger.