Is it "actively being used" or "being used actively"?

Solution 1:

The two sentences mean different things. The first sentence means that X is actually using M rather than just having it reserved for his use: the second means that X is using M in a very energetic manner. The reason is that the adverb is closer to the auxilliary verb 'being' in the first one so tends to modify the whole compound verb but is closer to the root verb 'used' in the second one so it tends to modify the root only. Please note, though, that this only applies to a very small number of adverbs where the adverbs have two different meanings in different contexts. It wouldn't matter which of "M was being carefully used by X" or "M was being used carefully by X" you used the meaning would be the same.

An example might be a cross trainer in a gym. A group might have booked a set of equipment for an hour for circuit training so all the pieces of equipment are 'being used' by the group but if no one is on the cross trainer when you look into the room it is not 'actively being used'. If someone was using it lethargically it could be said to be 'actively being used' becasue someone is on it but it is not 'being actively used' becasue they aren't working hard. On the other hand if, when you look into the room, someone is pumping away energetically on the bench press is is 'being used actively' as well as 'being actively used'.

Having said that 'being actively used' is quite restricted in its application. You are most likely to see it in analysis of the usage of equipment. For instance there could be a time meter on the cross trainer which would show how much time people had spent on it in total since the last time it was re-set. You could then say that it had been booked for 5 hours in a given day (it was in use for 5 hours) but was only 'actively being used' for 220 minutes in that time. That could matter for warranty reasons or for maintenance schedules.

In your case I would, as Jim and Old Brixtonian say, use 'currently being used by X' which would cover all eventualities, including time when it was reserved but actually idle.