I said try maybe it work.
Now it seems to be clear.
I have an Idea. Use two Diode in serie (1n4007 for exemple). Since each one drops 0.7V y'oull get 4.6V. The PIC will operate correctly since, as far as I remember the 16f84 require a voltage supply ranging from 3.7 to 5 V.
Yes.. i was too about to sugest the same point sugested by "hameeds01" The diode will drop the 6 volts to 5.4 volts which can be used to drive PIC directly .But ensure that in further use the voltage will go down below 5.4 and not rise above that (May be during charging if the 6 volt source is a battery)
Or as your requirement is only to drive a PIC micro, you may use a resistor + Zener diode combination to get 5.1V which will be safer compared to the later sugession. Cheers