General:
* Assisting
* Aiding
* Guiding
* Supporting
* Enabling
* Moderating
* Leading
* Coordinating
* Directing
* Orchestrating
More specific:
* Brokering (for negotiation or collaboration)
* Catalysing (for change or progress)
* Expediting (for a process or task)
* Smoothing (for a process or interaction)
The best synonym for "facilitation" will depend on the specific context. For example, if you're talking about a facilitator in a meeting, "moderating" might be the best fit. If you're talking about someone helping a group to make progress, "catalysing" might be more appropriate.
Here are some examples of how these words can be used:
* Assisting: The teacher assisted the students in understanding the new concept.
* Enabling: The new software enabled the company to streamline its operations.
* Moderating: The moderator guided the discussion and kept it on track.
* Brokering: The mediator brokered a peace agreement between the two warring factions.
* Catalysing: The new CEO's arrival catalysed a period of rapid growth for the company.