Apple dropped support for 32-bit applications with macOS Catalina. Lightroom 6 contains 32-bit licensing components and installers. It will not run on any modern macOS version (Catalina, Big Sur, Monterey, Ventura, Sonoma, or Sequoia) or on Apple Silicon (M1/M2/M3/M4) chips.

A completely free, open-source alternative heavily modeled after Lightroom's workflow.

Perform a complete clean reinstallation:

If you are searching for a "new download" of Adobe Lightroom 6, you are looking for a ghost.