To set this up the best way it should be mentioned that there are three kinds of signal to pay attention to (four if you count speaker level): instrument level, line level, and mic level. Instrument and line do not use the same kind of cable (hi-z and low-z respectively). Mic and line level signals use the same kind of cable but typically go to different types of inputs on a mixing board. A mic signal is quiet enough to require amplification...hence mic preamps....and a preamps job is to boost the signal as cleanly as possible up to line level. Synths always output signal at line level.
SO....with that background....
As jungleheat mentioned, two heads are better than one, but a single could possibly work if you are only using one of the three sources at once. I first set something like this up and ran loops of the synth while playing the bass at the same time into a single amp and it was a garbled mess. So I split it up into two heads and cabs and it was much clearer.
The simplest way:
One bass, one synth, one amp (with effects loop) & you'll need a mixer:
Run bass into amp input (instrument level)
Run send of amp effects loop (line level) into mixer
Run output of keyboard (line level) into mixer
Run output of mixer (line level) into amp return, and insert house's DI box here if they have one/need one.
The other simple way:
One bass, one synth, one amp (no effects loop) & you'll need an ABY box and an Xamp:
Run bass into input 'A' of an ABY switcher (whilwind makes one for about $60...these have two inputs, one output, and a switch to select either A/B and a switch to select "Both")
Run keyboard into Radial Xamp box or similar (takes line level down to instrument level cleanly). Adjust output pad to match signal level of bass so keyboard isn't louder or quieter than bass
Run output of Xamp into 'B' of ABY box
Set ABY box to "Both"
Run output of ABY into amp input, and insert house DI here if needed
The better way:
One bass, one synth, two amps & you might need an Xamp box:
Bass goes to its own amp and keyboard goes to its own amp.
Depending on the type of amp used for the keyboard:
If amp only has instrument input...use an Xamp for best sound quality (if you plug a line level source up to an amps instrument input it sounds like crap)
If amp has effects loop, plug keyboard into amps return - effects loops are at line level and you are basically bypassing the amps preamp and using only the power amp.
If amp is an actual keyboard amp (like Roland's KC500) it probably has line level inputs so you just go straight in from keyboard.
If using house DI's in this scenario, you will need two because the signals never get merged. But they usually have several.
So moral to the story, if the guys rig sounds killer then he is also probably being mindful of plugging up the right kind of signal to the right kind of input and being mindful of what is at line level, mic level, and instr level. My guess is he is running a bass into one amp&cab, and running the DSI synth, sampler and Akai box into a mixer and sending the mixer out to a power amp into the other cab. It looks like he is using a DJ style 4 channel mixer with a crossfader in the first photo....just under the yellow DSI Mopho (tasty piece of kit that one is BTW). If he needs them, he would insert one direct box between his bass to amp run (after any effects, and in the effects loop if he has one) and another between the mixer output and power amp input.