Using the smart wrench and socket wrench, remove the nuts that are holding the connector to the old brake line.
After taking apart the connector, slide the screw off the brake line.
The nut may be difficult to remove if it has not been removed for a while.
Keep in mind the order the parts came off the connector. This will make reassembly easier.
Remove the cable housing from its holders.
Slide the housing off the brake cable.
Remove the second cable housing from its holder.
Unscrew the other end of the housing from the brake.
Remove the housing from the cable.
Apply pressure to the brake to reveal the end of the brake cable.
Remove the cable from its holder within the brake.
Pull the remaining cable through the brake.
Flip your bike to make the brake housing more visible.
Insert the new brake cable into the brake housing.
Slide the cable housing onto the new cable.
Re-insert the housing back into its holders.
Slide the rear cable housing onto the new brake cable.
Re-insert the housing into its holders.
Slide the screw and washer onto the end of the brake cable.
Slide the connector of over the screw and tighten the nut and washer on the other end by hand, so it can slide along the brake cable.
Flip bike back right-side-up.
Slide the connector up near the housing holder. About an inch between the connector and holder should be fine.
Using the smart wrench and 10mm socket wrench, tighten the nut so it grips the brake line firmly.
Using wire-cutters, cut the extra cable so only about an inch remains.
You can recycle the old brake cable for this.
Insert the end of the brake cable with a "nub" into the slot on the rear left brake.
Slide the cable onto the slot on the connector.
Slide the other end of the cable into the holder on the right rear brake.
Pull the cable to clamp down the brakes so they almost touch the rim of the wheel.
Tighten the screw so the cable does not come loose.