How much current at 12 volts dc can 3 #16 ga wire handle 12 ft long all tied together?

First of all, hopefully this is just a theoretical question. Even though I'm not an expert, I can assure you that in practice it's very dangerous (and against any reasonable electrical code) to rely on multiple separate (i.e. individually insulated) parallel wires to handle high currents. If one wire fails, the remaining wires will be forced to carry all of the current, but no circuit breakers, fuses, or other safety devices would be tripped. This is likely to cause a fire if the current is beyond their capacity. If possible, you should use a larger single wire instead.

Secondly, the DC voltage (12-volts) and wire length (12 feet) are irrelevant with respect to ampacity.

Finally, the answer to your question depends on the type of wire and the environment in which you run it, but you should be able to look up the current capacity of #16 wire of whatever type you have with a simple Google search. In theory, the DC capacity of three such wires run separately should simply be three times as much as a single wire. Or, if you can only find information for larger wire sizes (like #14, #12, etc.) then consider that three #16 wires have a total cross-sectional area (and, therefore, DC current capacity) that's somewhere between #11 and #12 wire. So you can just use the numbers for a single #12 wire to be conservative. For example, if this was plain ol' NM-B copper (a.k.a. Romex) or THHN copper, the maximum current capacity should be around 20 amps.