Disk Utility is not used for reinstalling macOS. Disk Utility is only used to repair file systems and permissions, to partition & format drives, and to create/restore .dmg images.
You need to boot Recovery Mode, from a bootable macOS USB installer, or from the original OSX DVD that shipped with the Mac (or possibly a retail version of the OSX 10.6 DVD depending on the exact model of the Mac). Once booted to one of these installer media there should be an option to "Install macOS" or "Reinstall macOS".
What is the exact model of your Mac? You may be able to get this information by clicking on the Apple menu and selecting "About this Mac" or by entering your serial number here or here.