I have a question regarding Peace Machine's trait.

SUPPRESSION FIELD: If a character would take 4 or more damage, it takes 3 instead.

When a character is hit with 4 damage or more. Does his damage reducers "invincible, invunerable, impervious, toughness" came into play before or after the SUPRESSION FIELD?

Before.

You apply reducers while determining the finalized amount of damage to be taken and then clicked.

Core Rulebook, page 15:
Peace Machine's effect would kick in during step 3 of the damage sequence, after you have calculated the final (and possibly reduced) amount of damage being taken from step 2.