What is the best way to hang a very heavy pic on patio in strong winds

hard mount it with screws to the wall

Do you have siding you can hang it on? They sell special hangers that you can use to hang stuff on siding (it hooks on between the siding slats) and is probably pretty sturdy.

What are the patio walls made out of? What material is the picture/frame made out of? Is it outdoor weather proof?

If your siding is vinyl, the weight of the art may make it sag unless you anchored it into studs. You could mount 2 boards to the studs and then mount the art to those boards. If you have an overhead structure you could suspend it via wires and also anchor it on the bottom with wires. If you don't have o'head structure you could use some kind of planter configuration where you had posts anchored in and then attach the art to the posts but you would need to have a very heavy base to assure that it didn't blow over.

'Sounds like the picture is quite heavy. . . I would go with Marty's suggestion to hard mount it with screws into the wall siding. You will need extra long screws to grab on to any lumber behind the siding. Also, keep in mind that anytime you pierce through the exterior siding, there is a risk that you might get water eventually going into the holes. I suggest that you use rust proof screws, as they will be easier to remove.

No question is ever stupid. The best way to start learning anything new is to begin asking questions.

Where I live, using an example of hanging a frame on a wall, hard mount is putting the screw directly through the frame, then into the wall, attaching the frame securely against the wall surface.

Soft mount means mounting a screw into the wall, then hooking either a wire on the back of the frame or a hole in the back of the frame over the screw. Hard mounting is far more wind resistant.