I have a Lumix DMC-FZ300, my silent mode is off. The flash and shutter type are both grayed out and my shutter type is stuck on electronic shutter so my flash won't work. How do I make it so neither are grayed out?
4K Photo Mode forces the shutter to electronic. In any case, the flash simply cannot keep up with 30 FPS shooting.
The 60 FPS Burst mode which captures images at 60 FPS also forces the shutter to electronic.
Should none of these apply, Resetting the camera is a decent option. You will have to set it up again but that will make you figure the culprit.
There's actually a separate setting to control the shutter type.
Menu > Rec > Shutter Type
Below is a link to the page in the user-manual, in case you would like more information.