2008 Chevrolet Malibu brakes are clicking when stopping

This is going to be difficult to diagnose without being right there, but there are some things you can look for that will help. First of all, I assume you only hear this once unless you change direction again. There's two common things to consider. One is that a lot of manufacturers are having trouble with rubber bushings on their suspension parts. Typically a worn one will cause a clunking noise repeatedly each time you apply the brakes, or when you hit a bump, but not always.

More common is a loose brake pad or a drum brake shoe that hasn't fully returned. Your car was available with drum and disc rear brakes. You have to tell me which one you have. Disc pads can cause a click when there's a gap between them and their mounting surface. That's caused by grooves worn into the mounts, and is aggravated when a do-it-yourselfer replaces them and doesn't use a special high-temperature brake grease. At the mileage you listed, normal wear is likely to be the cause and nothing more. The clue that can help identify that is to hold the brakes lightly applied when you shift to reverse, then release the pedal as soon as the car starts to move. That will make the pads shift position against the other mount and they'll be held there as long as the car is moving. When you apply the brake again, the pads will already be against that mount so they won't suddenly move and click.

If that's the cause of the noise, it may be irritating, but it's not a safety issue. Drum shoes can do that too, but that either means they're seriously out-of-adjustment or they're being prevented from fully returning to their anchor pin because a parking brake cable is rusted in the partially-applied position. That is a real big problem on Ford products as little as one year old. It's not as common on other brands, but it has to do with age, not mileage. If you live in a place where they throw a pound of road salt on an ounce of snow, like I do, rusted cables are real common. There's two things for the mechanic to look for regardless if new shoes were installed or not. Both shoes have to return fully so they're touching the anchor pin on top, and the parking brake strut bar between the two shoes should be able to be pushed forward against the pressure of the anti-rattle spring about 1/8". If either of those is not the case, the parking brake cable for that wheel is rusted or the main cable is adjusted too tightly.