WIRING WIRE INSIDE THE FURNACE HAD BURNT AND I NEED SOME HELP REWIRING THIS UNIT

so you need to check the thermostat wiring it seems

This is not going to be easy. Check the wiring in the wall to look for the third wire. If they did not run one, you have to run new wire to the furnace and thermostat. If they stapled that wire to the walls inside studs, then it is going to be even harder to run the new wire. Once you run that new wire then you have to locate the connection in the furnace that has the common (c) wire for the transformer. Check you tube to see if the have any how to video.

The blue wire from the Ac goes to the y2 on the board for the furnace the yellow and brown goes to c on the board for the furnace and the last wire goes to y1 on the board for the furnace

Don't need the blue wire is common for the ac condsor unit what t-stat is it honeywell 4000 6000 8000 or one of rth models there is many t-stats as far as you saying fan stayes on check the auto / on section of the t-stst main wirers are RH/R-power W-heating Y-coolin G-fan

I’m happy to help further over the phone at https://www.6ya.com/expert/vincent_f7b7c5f4dedd2565

I can give you a start, For heat only, R terminal on furnace to Red wire to R or RH terminal on thermostat. W terminal to White wire to W terminal on thermostat. G terminal to Green wire to G terminal on thermostat. This will get you heat but not air conditioning.

The transformer is for the low voltage side of your furnace, you should be able to take the door off of the furnace and follow the wiring schematic on the inside of the door to wire it back correctly.

What are you wiring? Possibly we can help.

If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79

If you look at control box at roof unit, they usually use a separate set of wires for furnace. See what colors they are attached to at harness to thermostat. Some just follow other harness, and come out at thermostat. (bypass control box) Once you've determined which 2 they are, join them together & see if furnace starts, as it should. If it does, thermostat is faulty. If not, pull outside cover off & check voltages at furnace. I'm guessing by furnace model that your unit is approx 30 ft , but if it's a park model, you may have 24 volt system on furnace or 12 volt. Another way of confirming is to go to back of furnace where air intake grille is inside your unit, and locate 2 blue wires going to furnace & remove whatever wires are attached to them & connect them together. Furnace should start up.

Only 2 wires going outside.
Yellow from the thermostat and the common wire from the lv side of the transformer.

Hopefully there are markings on the old t-stat as to what terminal is what.
on the honeywell 8000 use the heat pump labeling and then the standard wiring would be
R- red
AUX-white
Y- yellow
B- O/B
C- black
G- green
There should not be a bare wire, it probably just has the insulation stripped back way too far.
You should probably open the furnace and compare the terminal label in the furnace to the wire color. normally yellow and blue pass through the furnace and are wire nutted to wires going to the outdoor unit. In the furnace the white wire will connect to the w or w1 terminal. also, you will need to set the Honeywell stat to have the following parameters.
170-7
190-1
200-0
other parameters that I did not specify, you may read the manual and make your own decision but I recommend factory settings for the other parameters