I haven't modified a Sony NEX camera with a hardwired jack in a while since there are several new mirrorless SLRs out there with remote jacks (our article on mirrorless SLRs for skydiving). This article just shows the picture differences from the NEX7 mod since it's pretty much the same thing.
Previously, I've disassembled and modified a Sony NEX-5 and Sony Sony NEX-7. The NEX-6r disassembly is not much different than taking apart the NEX-7, but there is one new clip that you'll need to carefully use a "Spudger" on. To dismantle the camera, simply remove the screw above the USB connector, the one under the flash connector, two from deep within the battery port and one underneath the neck strap connector next to the shutter switch. At this point, the top should be fairly loose but stuck above the SONY lettering on the front. At this point, gently pry this plastic out to dislodge the clip as seen below. Use a plastic spudger or pick for this.
Now that the top is off, you can wire it as shown below. Black is ground, red is shutter and yellow is focus. Note that this switch is very sensitive. Do not get flux in it or it will be destroyed. I have not been able to find a replacement, so if anyone knows the source, please comment below. It's around a 3.7mm to 4.0mm 6 pin, where pins 2 and 4 are connected to the top. I always ohm these out before closing it up. I also use a drop of crazy glue to hold down the wires somewhere on the assembly since we are taking this in free fall.
I removed the back, just like the NEX-7, so that I could run the wires to the bottom. There is a single screw under the USB cap, two on the bottom (the one under the 1/4-20 is not necessary to remove) and one shallow screw in the battery compartment. The back should slide right off when the display is raised up.
This is how I ran the leads. Note that I drilled 3 tiny holes and affixed the connector with epoxy so it would not come off from a yank.
I tucked the excess between the battery bay and the hand grip, then put the camera back together.
HYPOXIC is obviously not liable for ruining your camera or any other negative things that may result from using these instructions. Use at your own risk. Please read the Adding a hardwire shutter release to the Sony NEX-7 before performing this so you get a full description. This article is just bare bones changes between these cameras.