Is it possible to break any given matter down into protons, neutrons, and electrons and then reorganize those particles into any other form of matter? I was reading about this somewhere but can't find the site now. It was talking about using 3d printers in the future that can intake any matter (dirt, garbage, etc..) and deconstruct it on the atomic level down to just electrons, protons, and neutrons and then use those left over subatomic particles to create anything by rearranging those particles into the needed formation for whatever it is you want to make. This would surely have a huge impact on the way we live since you'd be able to use your own human waste for example to make anything you'd want as long as there were enough particles. But is this theoretically possible? 
 A: Let's start with the molecular case. Dissociating atoms in molecules into free atoms is possible by heating them enough so that all the bonds break; this bond dissociation energy is less than about 1 MJ per mole of a particular bond in the substance. Then in principle they can be reassembled into other molecules with the same atoms  and one regains their enthalpy of formation. The challenge here is separating out the different atoms from each other (for example using a plasma mass spectrometer) which has an unavoidable thermodynamic cost that is the negative of the Gibbs Free Energy of mixing (for a 50% mixture this is about 5 kJ/mole). Plus, of course, actually doing the assembly operation using suitable atomically precise manufacturing. 
On paper, the energy cost would just be the difference between the dissociation energy and enthalpy of formation, plus the separation energy cost minus the mixing enthalpy. Ideally all of this is adiabatic processes gently nudged towards the desired outcome with a minimum of entropy increase. In practice this will be a lot more since these processes are not done perfectly: there are huge swings in energy and temperature, and these cause entropy increases that have to be "washed away" using waste heat. The above "heat to disassembly, separate, cool and reassemble" approach will likely have an energy cost comparable to the involved energies a few times over.
The nuclear case is exactly the same. You can photodissociate $^{56}$Fe into 13 alpha particles and 3 neutrons by hitting the nucleus with 124MeV photons; by heating matter nuclei to $10^{10}$ K it can hence be converted into free nucleons and alpha particles that can then in principle be separated, cooled, and fused into other isotopes with a total energy cost/gain depending on differences in binding energy. The thermodynamics looks the same: you will have to pay a minimum cost around 5 kJ/mole of nucleons just to separate the types and most likely pay a huge cost for the whole process.
If you have the wrong number of nucleons you could go even higher to the Hagedorn temperature $2\times 10^{12}$ K where baryonic matter "melts" and get newly minted particles out of the quark plasma, but this will likely waste a lot of it as uncatchable particles like neutrinos or anti-leptons left after pion decay (when you get antimatter as a waste product it is a hint that you are doing something wrong!)
The moral is that matter is interconvertible. But rearranging it in the "obvious" way is very entropy and energy-intensive. Smart manufacturing finds the least energetic transitions where every step is close to thermodynamically reversible. Typically that means keeping bigger parts as intact as possible and only change what needs to be changed: most nano-manufacturing will likely involve recycleable standard parts, with the most energy-intensive process being making those standard parts (that are then packaged as feedstock). Of course, to a user it might still look pretty magical. But the device will still have a power cord, a hefty cooling fan, a feedstock input... and likely regularly annoy us with "out of thulium error" and "graphene jam" error messages. 
A: Yes, this is theoretically possible. In fact, it has already been done for certain transmutations. But even when turning lead into gold, at present the cost of the process (at least that process) is prohibitive.
