Need to know how to wire a marshell speaker cab

First it is certain that you would not want to plug both outputs of the stereo power amp into one speaker combining both channels into the same speaker. (see image from manual below - also link to manual)

Next I would be very concerned about only using the one side of the main amp out as it could cause an unbalanced load, or you could be driving the load into dead air connection and any of these conditions are destined to cause premature failure of the power amp.

Taking a quick scan of the manual for this unit, it appears what is pretty common to most powered mixers, hook up two matched speakers/loads to each chanel of the output.

Your best bet is to shed those monster cabs, there really is no need for them especially with this sized powered mixer, and get yourself a nice pair of full range cabs like EV1202;s, EV SX300's, or some nice 2 or 3 way 15" JBL's/

Just my opinon.

Link to Yamaha EMX 312 Owner's Manual:

Yamaha EMX Series Owners Manual

Stereo and bridged mode selects automatically. Stereo mode gives 4-16 ohms per side. Bridged mode is only from 8-16 ohms. This impedance match is created by the combination of speakers you use. If you link any speakers, the wiring is usually going to be in parallel because of the sockets wiring in the cabs. Any time you link 2 speakers in parallel, it cuts the impedance in half. Remember that in bridged mode, do not link 2 8 ohm sets together because this will create a 4 ohm circuit which it will not allow. This can only be done in stereo mode. It is ok to use speaker combinations of higher impedance, but never go lower as it would cause damage to the power amp.

Get the Speakons to 1/4" cables. If you're concerned about grounding, make sure the amp is turned off before plugging or unplugging the speakers.

Make sure you are using this on a three wire grounded receptacle. If you are on an old two wirepower system, have a ground installed in the receptaclel you are using. If you are on a grounded circuit, then exercise your warranty for repair/replacement.

Most schematics won't even have any colors listed... so let us have you try this:

Find a system ground someplace like the sleeve of a 1/4 inch jack... Using an ohmmeter check for continuity to the available wires that are disconnected. ASSUME that those showing a low resistance will go to the "-" terminals of the drivers. If you have say a black and red... expect that the black will be one of the grounds... often the red then will be the (+) of the woofer. If you have whites and yellow... OFten the white will also have continuity to ground and be the (-) for the tweeter and the yellow then to the (+). Now since your speaker has 4 woofers we need to be careful to wire then correctly to get the 4 ohm impedance of the cab. IF each woofer is 4 ohms impedance, then we need to wire them in series-parallel. The shell of input 1.4 inch jack will likely go to black wires... two of the speakers will have their (-) terminals connected to these. The tip of the 1/4 inch jack will probably connect to one or more red wires. These will connect to the (+) terminals of the OTHER TWO woofers. Next one of the available (-) with no connections will tie to the (+) terminal of one of the first two woofers. SImilarly the remaining (-) terminal of one of the woofers will tie to the last (+) terminal that is vacant. Note the + of the horn will tie probably to the High level pot and this will tie to the crossover someway.
Here is a site with general schematics.

http://www.bcae1.com/spkrmlti.htm

Yellow should be the positive. Try plugging in and reversing. The louder of the two is the one in phase and the correct wiring. If the speaker is pushing out when playing , it is in phase and correct also.
The distortion problem could be a speaker going out. It may not be totally blown, but may be verging.
Holding your hand out as wide as you can push against the speaker lightly. If there is a rubbing or scratching sound, the speaker could be damaged.If it moves freely, and there is no scratching its okay.
Another possibility is the clean channel may have a channel volume set to high. Make sure the clean channel volume is set lower than the master volume otherwise you can get distortion on that channel too.
Good Luck.

Wiring harness connector to the power tube section is fried. A common problem with all bugera amps and many other companies also. A cheap fix. You can order the part you need from newark.com or call 1-800-4newark the part number is sku#85c0290 mfr#09-91-0500

Weather of not you can use this speaker as an extension cab depends on a number of things. First, what amp are you planning you use for it? What is the minimum resistance for this amp (2ohm or 4 ohm probably). Second, what is the primary cab you are using ans what is the resistance on that? (2ohm, 4ohm or 8ohm).

Is there just one speaker in you proposed extension cab? The goal is to have all the speakers wired in parallel without lowering the resistance to a point that will damage the head. So if your amps minimum resistance is 4ohm then your cabs will have to both be 8ohm, running in parallel the overall resistance will be 4ohm.