The half-life of carbon-12 Let us denote the half-life of the proton by $Y_p$. (There is, of course, no experimental evidence that $Y_p<\infty$, but there are theories that assert it, so this is really a question about those theories).
The question is: what, in that case, is $Y_C$, the half-life of a carbon-12 nucleus?
A naive answer would be that since $^{12}C$ contains six protons, $Y_C=\frac{1}{6}Y_p$.
However, protons do not decay. Quarks do. Since neutrons are made of as many quarks as protons are, they should decay into non-baryons just like protons. Since $^{12}C$ contains twelve nucleons, that makes $Y_C=\frac{1}{12}Y_p$.


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*Which is it? $\frac{1}{6}Y_p$ or $\frac{1}{12}Y_p$?


There is a hidden assumption in all this: that the half-life of a quark is unaffected by the baryon or meson in which it finds itself. On the other hand, the half-life of a neutron is strongly affected by the nucleus in which it finds itself (or doesn't).


*Is the assumption of environment-independence correct for the decay of quarks into leptons?


There is one more assumption. Protons and neutrons are each made of two different kinds of quarks. 


*Do the theories that make quarks decay into leptons assign identical half-lives for this process for both up quarks and down quarks?

 A: Half-lives of bound systems don't usually have any simple scaling laws of the kind you have in mind. The half-life would depend in part on the phase space available to the particles that were produced, as well as factors having to do with nuclear structure. However, this decay is a rather high-energy process. Decay of a proton into a neutral pion and a positron has a $Q$ value of 802.8 MeV. Because a 12C nucleus has a different binding energy than a 11B nucleus, the $Q$ value of your decay would be different, probably lower by on the order of a few MeV. But this is pretty small compared to eight hundred MeV, so it would probably have a small effect. So I would guess that in this example, because of the disparate energy scales, the fact that the proton was bound inside a nucleus would have little effect on the half-life.
For similar reasons, I would expect there not to be much difference between the contribution of the neutrons and that of the protons. So 1/12 of the proton's half-life is probably a pretty reasonable estimate. 
