Connecting C-wire in the furnace (C terminal already taken up)

that furnace is a typical carrier/bryant control with terminals

C Common

Y Call for Cool (call for A/C)

GC Fan Cooling (high speed)

GH Fan Heating (low speed)

R 24v power

W Call for Heat (call for furnace)

The jumper between R and GH is for thermostats that do not have a High and Low blower speed selection. (which is most of them, yours probably) When it is there the control board works "normally" in that if you call for heat the low speed blower turns on if you call for cool the blower goes into high speed. It should only be cut if no A/C is present at all, and the thermostat is heat only and has a low and high speed fan for those weirdos who want to turn the fan on high when running the furnace.

You can connect the ecobee thermostat G wire to either GC or GH depending on whether or not you want to be able to turn the fan only on, and what speed you would want to run it at if you did. (for example you want to run it in circulation mode in the fall or spring) Probably you would want to run the fan at low in that situation so I would use GH for the G terminal.

The other terminals are normal, R to R, C to C, W to W, and so on.

Now here is the meat/heart of the problem. THERMOSTAT WIRE COLORS ARE BLINKIN MEANINGLESS!!!!!!!! There are TRADITONAL colors, they are:

G Green

R Red

C Black

Y Yellow

W White

But NEVER NEVER NEVER N_E_V_E_R!!!!!!!!!!!!! Trust them E_V_E_R. ALWAYS validate BOTH ENDS OF THE CABLE!!!!

You have that cable with the red going to C and the white going to Y. What is it for? I dunno. Maybe someone put a motor operated pinwheel on top of the house that turns on when the AC is turned on. You certainly better trace it out and find out what it is I think. It MIGHT be going to an AC unit that is completely separate from the furnace such as if someone put an A/C on the furnace that was made by Johnny Kewel not Carrier. If your furnace has a Carrier A/C on it then the A/C is certainly controlled by the furnace microprocessor not by that oddball second wire and the connections would be to a header buried in the furnace not some hokey extra wire.

Anyway I'm assuming the wire on the right is going to the ecobee. In that case the unconnected C wire needs to go to.....drumroll please..... C

I see several unconnected colors you have a black an orange a blue and maybe a thin little pink in there. The installer probably had whatever the heck extra coil of thermostat wire in his truck. If you followed the "color codes" then use the black wire for C. But DO NOT BLINDLY TRUST THE COLOR CODES. Make sure that the alphabet matches at both ends the furnace and the stat. If you want to be a decent person you would follow the traditional color code in your own wiring so that the next guy who comes along isn't screwed over. And that next guy might be you if that ecobee breaks down.