The American Heritage dictionary gives the meaning of the Greek word reported in the Liddell-Scott-Jones Greek dictionary:http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dsunqetiko%2Fs
But this is apparently based on just one attestation of the Greek word in ancient Greek literature. It seems to have been a word without many attestations, although it is a compound word that is based on elements--a prefix, verbal root and suffix--each of which is very common in Greek, and the meaning is very transparent to anyone who knows some Greek.
Based on the elements out of which it is compounded, it means something like "pertaining to putting together." In fact, the English words "compound" or "compose," or, better yet, the participles "compounding" or "composing," are very close to the meaning of the Greek. In the attestation listed in LSJ, it seems to refer to a certain "compounding" person, i.e., one who is skillful at compounding or composing or putting things together.
Of course, that doesn't mean that the English word "synthetic" is necessarily limited by the meaning of the ancient Greek word from which it is derived.