6 volts at the coil is good, only if the points are open. So check at the coil wire and condenser connection at the distributor. Should also be 6 volts with the points open. If not, check the distributor wire connection at the coil. If that is tight, the next step is to disconnect it at the coil and check that wire for continuity. That is, zero ohms between the coil end and distributor end of that wire. Those wires have been known to corrode internally and go open from that and flapping in the fan breeze.
If that checks good, hook the coil wire up again, put the voltmeter on the distributor side of the coil and bump the starter until the points close, as indicated by a drop in voltage at the coil from 6 volts to near zero volts. If you can not get it to drop, the points aren't making ground. Points could be fried or grossly out of adjustment; pigtail to points loose or broken, distributor housing not grounded to block.
If you do get the voltage to drop, leave the motor in that position and go back and check voltage at the ignition switch side of the coil. Should be about 4.7 volts, due to IR drop across the ballast resistor under the dash. If it drops much below 4.7 volts, the coil is drawing too current. probably due to windings shorted internally.