How did Ebbinghaus decide on his number of words in a series?
If you read Ebbinghaus' article carefully, you will note that in Chapter III. The Method of Investigation, Section 13. Establishment of the Most Constant Experimental Conditions Possible, Ebbinghaus gives the following third of seven rules "for the process of memorising": 


  3 . Since it is practically impossible to speak continuously without variation of accent, the following method was adopted to avoid irregular variations: either three or four syllables were united into a measure, and thus either the 1st, 4th, 7th, or the 1st, 5th, 9th ... syllables were pronounced with a slight accent. Stressing of the voice was otherwise, as far as possible, avoided.


This rule results in 3- or 4-syllable substrings. Of course the whole string of syllables to be memorized must be a multiple of either 3 or 4, if it is to follow this rule.

Your answer is: Ebbinghaus chose 8, 12 or 16 syllables, to keep the experimental conditions constant.