When I put the car in gear and begin to go forward or back,a rattling noise is present.It goes away as the car accelerates.My brother (a mechanic type guy)looked under the car as I stepped on the accelerator,(in park ,of course),and saw nothing shaking or loose ,(mainly with the exhaust)…take it to an actual mechanic?
The first thing to inspect is the exhaust system, not visible from under the hood. Usually the HEAT Shield over the catalytic converter works itself loose. Don’t remove the heat shield, it is there for a purpose, to keep the floor of your car from overheating. My brother-in-law lost his on a Ford and ended up with the car on fire from the rugs catching fire!
You could also have a few loose or missing clamps, allowing the exhaust pipe to wiggle around and come in contact with the underbody.
I am not there to rule this out but early second generation Malibu’s had noisy lower control arms. There are TSB’s on this issue.