LED light install with Red, Black, White, ground wires

I'm looking to replace one of my garage lights with a new LED fixture. I have two lights, one for the first two garage doors and a second for the third bay. I have two light switches, one controls the first light and the other controls the second light. They work independently and not like a three way switch.

I pulled the light receptacle down for the first light and t has the black hot plus two red and two neutrals (white). I'm assuming they wired it that way so they could jump the wires from the first light over to the second light light. Not sure why they didn't run separate lines for each light and each switch. I've never seen this type of setup before. The LED light only has the white, black, green wires.

How can I hook up my LED fixture? Is it even possible in this scenario?
Here is a picture I took of my receptacle and then a screen shot of the installation instructions from the LED light.

 

Welcome to the forums.

Connect the two white wires together and add the fixture white wire.
Connect the two red wires together and add the fixture black wire.
Connect grounds.

Be careful...... handle the white wires as hot when removed from the fixture as they may be feeding a load between them and the black wire.

 

Thanks, I'll give that a try and switch off the circuit breaker first.

I sill don't get why they used the red wires like this
unless that's all the electrician had at the time or maybe it was due to the light receptacle having the two mounting points for both the hot and neutral.

 

That is three wire cable with ground. It's commonly used to wire an always live/switched circuit or two switched circuits. In your case... it's two circuits. One switch powers the red wire and the other switch powers the black wire. The white neutral is shared.