I have a dryer that requires a 4-inch duct, and a 3-inch wall hole..?

It's not advisable to reduce your 4-inch duct just to fit an existing hole. Doing so will reduce the air flow and introduce a whole bunch of potential problems you won't want.

Make yourself a circular template out of thin cardboard by drawing a 4 1/8" circle using a compass. Cut out the circle with scissors. Place the template on the wall and adjust its position to avoid cutting into any framing members. Tape the template in place and trace around it using a Sharpie ink marker.

Push back any insulation from the area to be cut. Look to make sure no electrical wires or plumbing pipes are in the area to be cut. Cut out the circle using a keyhole saw or a jigsaw. If the wall is finished (has wallboard on the inside) cut that side first, then drill 2 or 3 small holes from the inside through the exterior siding in order to locate the template on the outside. The drilled holes should be in line with the edge of the inside hole. Then mark and cut the exterior.

Be sure to install the proper size vent hood on the outside and caulk it around the top and sides. If the inside wall is finished, you can (optionally) install a standard trim piece made to slide over the vent pipe that will cover the wall cutout.

Good Luck.

Look for a 'reducer' to go between the 4" duct and into the 3" hole.

If you reduce it, it'll clog up with lint very often and quickly. Make the hole bigger.

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