When my washing machine drains the water after the agitation cycle the overflow pipe backs up and floods my garage. Also the water will back up into the sink. We have used drain clogging chemicals on both drains and snaked the lines but nothing has changed. We have city sewer so nothing to have pumped and no other drains are backing up?

You still have a block in the line and didn't clean out far enough. Try cleaning from the sink. Are they on a common drain line? Washer drain lines are notorious for clogging due to lint and dirt that gets pumped out into the line, particularly if a small pin or wire goes out.

Jgardner...

As mentioned above, the drain line is still clogged. Have you tried using an electric snake machine? If not, go to a local tool rental store and rent a medium snake machine and purchase some leather gloves and a pair of safety goggles. Then snake the drain down a large cleanout or go down the washing machine vent coming out the roof (if pitch of roof permits).

Otherwise, if you are trying to snake through a PTRAP or PTRAP cleanout, I'd also recommend cutting a new full size cleanout into the drain line and using hot water and the electric snake to clear/clean the drain line properly.

Good luck!

Mark