Explain them function or purpose of the following the eyes and the pairs of handmaid's

Sorry, I don't know what your question is asking here.

I believe the "eyes" primary function is to be a spy and report the goings on of their communities guardian's, aunts, Martha's, handmaids, wives, and commanders up the chain to the high command.

As for why the Handmaid's are always sent out in sets of twos, I believe it's just to discourage sneaky behavior. If they always have another set of eyes around them and they don't know if they are "true believers" or not they can't ever do anything out of line for fear of being told on. You see this demonstrated by the fact that they very seldom will even stray away from basic small talk, they will only say things such as "we've been sent good weather", because they're afraid if they say anything more personal it'll be reported and they'll be punished. I'm not a expert on this, but that's my take. I hope it helps.