The merge room objective is instructing you to merge 3 rooms together a particular amount of times.
For example, if the objective reads "merge four rooms", it means to merge three rooms, four times.
It does not matter what type of rooms you make, as long as they are merges of three separate rooms.
Also keep in mind that rooms will not merge together if they are different levels. For example, if you upgrade your water treatment plant, it will not merge with a joining water treatment plant, until the second plant is upgraded to the same level.