How do I fix my ranch king MTD ,when I turn the ignition on the selenoid clicks but the starter doesn't turn. I used a test light and tested everything and it all lights out. What could it be?

Sounds like a dead battery! Have you tried jumper cables from your vehicle to the Ranch King battery? If it cranks, suspect the battery. It may require recharging or more likely replacement.

Where is the solenoid located on a ranch king riding lawn mower 14.5 hp

Hi! leerenco7, welcome to AMHD :)

Raise the hood.
Look inside directly in line with the ignition switch.
Mounted on the inner wall above the battery or below the battery tray you should see one big red wire, and up to four others attached to two terminals depending on your tractors requirements.