Strip off 3/8 inch from the end of each of the cable's 8-3 gauge wires, using a wire stripper. Place each wire in the 8-gauge marked slot on the edge of one of the the stripper's jaws, 3/8 inch from the end of the wire. Squeeze the stripper's handles together, and pull the stripper towards the end of the wire to remove its plastic insulation coating. Repeat these steps with the cable's remaining wires, as well as the wires on the end of the second cable being spliced to the first cable.
Slide the bare end of one of the first cable's wires into the end of an 8 gauge heat shrinkable butt connector, so the bare copper end is fully inserted into the connector's central metal section. Open the jaws of a crimping tool, and rest the connector on one of the tool's jaws where it is marked for 8 gauge wire. Ensure that the tool's jaw rests 1/4 distance along the central metal section of the connector, on the side of the installed copper wire. Squeeze the crimping tool's handles together, to crimp the connector to the wire.
Heat around the half of the connector that the wire is inserted into, using a heat gun or paint stripping gun. Wait for the connector's plastic coating to shrink around the inserted wire.
Install the same color wire from the second cable into the other end of the connector, crimp it in place and apply heat. Continue in like fashion installing the other wires together from the two cables using heat shrinking butt connectors, installing them as previously described.