My 2006 Equinox is running rough and billowing white smoke from the exhaust. It appears to be water. What is the repair?

It sounds like it could be head gasket leak

If it is a head gasket, check with the mechanic and ask what may of caused the failure. Just sometimes it is the driving habits or other external causes. I don't know the driving habits or mileage or even the type of weather it is driven in. All that is a factor, and don't forget age of the vehicle. It is nine years old now, and a lot has been asked of the gaskets. Decades ago, head gaskets were a common failure on the old iron engines. Since the cranks no longer have been issued with cars, improvements have been made not only in the engine blocks and head design and materials, but the gaskets also for the most part. I'd say nine years is a good long run for them, though many last longer. If the engine has run hot or other factors, the heads can warp and cause failure. Running hot can be caused by i9mproper radiator fluid mixture, loss of fluid over time and not refilled, cold engines that under very cold temp outside can freeze the fluid, and it doesn't cool until a rush of coolant hits the water jackets and that can warp the heads. Many ways and reasons for a failure. So ask and if possible change driving habits and enjoy your Equinox.