Shorted a speaker wire together

Check for short circuit wiring on the speaker leads.
Either touching together or touching the body of the car.
It is designed to shut down to protect the internal amp.

Disconnect all the speaker wiring then re connect one at a time to isolate a wiring problem. Usually a short circuit to earth, car body, but be carefull no the touch the speaker wires together.

pretty much any amplifier can run any sub, so the question is not weather or not the amp can run them, it is how well the amp can run them. Those Pioneer subs are dual VC models and are rated at 600 watts RMS. You have two, so that would be about 1200 watts of RMS power you will need in order to power the subs correctly and to optimum efficiency. The amplifier model you have is rated at 600 watts RMS for a single channel at the lowest stable impendence. That power coming from the amp will be split two ways between the subs and divide the power to each speaker. So each speaker will be receiving 300 watts of power. So in short yes, your amp will power those subs, but they will only be operating at half their rated power. Your amp will be running at maximum power so it might get a little warm after a while. make sure you wire it correctly and keep the amp well ventilated if you decide to push it that hard. if you need help on how to wire them search the web for wiring options by typing into Google " how to wire two dual voice coil subs into amp". There you will find plenty of illustrations to help you decide.

Possible that a speaker short may have damaged one of your output channels. When that happens it is not common for the receiver to shut down to prevent further damage to other components.

Are we a little impatient?

It's pretty straightforward. Use one cable to connect the tape deck to the amp. Use another cable to connect the tuner to the amp. Use speaker wire to connect the amp to the speaker.

Well get yourself a digital volt/ohmmeter and trace them out. Plus and minus are not absolute. Just don't touch one to the other with power on. Reversal of them on a given speaker only changes its phasing. Web search: speaker phase test

With no attachment to any electronics - short the pair at one destination together ONLY for this test. Go back to the source end and use the ohmmeter to see which two conductors they represent. Mark them. Disconnect the short. Repeat for other speakers.

Since there are only the two conductors it's not rocket science to reconenct them. Did you short them together and damage the amp?

Hook 1 speaker to the white (+) and white/black (-) wires and the 2nd speaker to the gray (+) and gray/black(-) wires.

The green and the purple wires are the other speaker wires dont use them cut them so they are connected to anything and tape them with black electric tape so they wont short out and touch the chassis of the car by accident. Also dont let them touch each other too thats why you have to tape the exposed wires and insulate them. Many people forget to do that.

Remove the bridging links from the speaker terminals and run two equal lengths of speaker wire from the amp to the speaker. At the amp - speaker terminal, twist two of the same wires together. ( normally marked with a tracer color) Connect these into your left speaker output - terminal and tighten. Connect the two wires to both the negative terminals on the speaker. Repeat the same for the + side. Make sure wires are not shorting across the terminals.

If the amp is in protect mode, it probably has shorted output transistors. To eliminate other possible problems, do the following. I'll assume that you've checked the amplifier's on-board fuses.

With your multimeter set to DC volts, the black meter lead on the ground terminal of the amp (not on the point where the ground wire connected to the vehicle) and the head unit on (so the amp will have remote voltage applied), touch the red lead alternately to the B+ and remote terminals of the amp. If the voltage is below ~11 volts, you need to check the wiring feeding whichever line is too low.

If the voltage remains near or above 12v, disconnect all speaker wires from the speaker terminals of the amp and disconnect signal cables from the amp. If it powers up, the wiring needs to be checked. If it still shuts down, the amp almost certainly has shorted output transistors and will need to be repaired.

Let me know if you have any other questions.