Flip off the circuit the breakers to the exhaust fan and to your air conditioning and heating system.
Slip a hose clamp over one end of the flexible vent ducting. Attach that end of the flexible ducting to your exhaust fan's outflow vent pipe. Wrap the seal where the ducting fits over the vent pipe with foil duct tape.
Run the other end of the flexible ducting to your existing 4-inch ABS vent pipe.
Use your PVC saw to cut a section of the existing ABS pipe out. The cut will be the same size as the straight section of pipe on the ABS T-connector.
Apply PVC glue to the two straight ends of the ABC T-connector and then connect these two ends to the section of ABS vent pipe you cut out.
Slip another hose clamp on to the other end of your flexible ducting. Apply a small amount of PVC glue to the inside lip of the flexible ducting and then attach it to the T-connector. Use your screwdriver to tighten the clamp and solidly affix it to the ABS T-connector.
Restore the power to your vent fan and heating and air conditioner.