Answering "How many months of work experience do you have?" on grad school applications
As you are aware, this is hard to answer. Hours worked don't translate well to months, since you often think about things and are engaged when you aren't officially "on the clock". 

Of course the answer also depends on how complete you are allowed to be in reporting. If it is an open ended question, I'd suggest that you just list each activity with both (a) how many months you were engaged and (b) and estimate of how many hours per week (or whatever) you spent over that time.

But if you can create that list you can probably also reduce it to a range of months, something like "8-12 covering different activities at different times". You could use that if you need to give a short description. 

If you need to give a single numeric answer without caveats and some precision is required, just give your best guess based on the above, but be prepared to discuss it in any interview you might have.