かた
shoulder
kata
JMdict 1258950
かた肩shoulderもん揉んrubで
The object 肩かた (shoulder) comes first, then the verb 揉むもむ (rub) shifts into its te-form 揉んでもんで (rub). A bare te-form like this works as a casual, friendly request — "rub my shoulders" — without needing ください (please) after it.
hanamaru