Incorrect speaker cable connection can damage amp?

It doesn't seem to me that you're shortcircuiting outputs so it will not damage your amp. Connect your speakers correctly to either one of sets. In lots of cases extra set exists for biwiring with the separate set of speaker cables(or wires). If you have a tube amp you should check if the two sets are designed to work with speakers that have a different impedance.
In well-designed tube amp there will be an output stage fuse that you can check, but first you should connect them properly and listen.

I'm still undefined about wheather the A, B are the sets of speakers(which I mostly believe) or set1,set2.

It looks like you either connected them out of phase (plus (RED) to minus (black), and minus to plus) which will do no damage, it just may sound a little thin; or you connected the left channel to the the right speaker, and vise-versa, which is OK also.

If you connected one speaker in-phase and the other out of phase, some sounds will just cancel each other out (in the air).
This is OK electrically also, it just won't sound right.

Most high end amps have protective circuitry or fuses to protect against "user stupidity"! Don't take this personally, as I was referring to myself! In audio, we all do`dumb things over the course of our listening pleasures throughout the years! If this is your first tube gear, PLEASE BE AWARE THAT THE VOLTAGES INVOLVED CAN BE LETHAL, EVEN IF THE UNIT HAS BEEN TURNED OFF FOR A WHILE!!! Let the unit play, at low volume, with the power OFF until the sound ceases. Be sure that no part of your body is grounded (touching the metal chassis, two parts at once, metal equipment rack, or turning on a light switch) when replacing tubes or fiddling around inside. Happy Tunes!

Folks, I think I did not explain things well.

Instead of thinking things horizontally, I thought of them
vertically, so the two ends of each speaker spanned both the
set1 and set2 amplifier speaker connectors! Is this better now?! That is why there was no sound to be heard!
The L of a speaker cable was connect to the L of set1, but
the R of the same speaker cable was connected to the L of set2! Sorry, but that is how things were laid out on my solid state amp!

Thanks again

Your explanation is still a little confusing: cables don't have a left and right; they have a positive and negative. It sounds like you attached both to positive (or negative) terminals of your amp. In other words, you've failed to create a circuit through which the AC can flow, hence the lack of sound. But given that nothing's flowing, it's unlikely that you're doing any damage to anything. (Except perhaps your pride, but we've all miswired something in our lives.)

No, you didn't damage you amp. Unless you have a connection from b+ to b- (between the positive to the negative) no current can flow, hence the lack of sound.
Thus, it can have no effect on your amp.

Damon