The fact is that these six protons and six neutrons have a larger mass when they're separated than when they're bound together into a carbon-12 nucleus. This is true for all nuclei, that the mass of the nucleus is a little less than the mass of the individual neutrons and protons. This missing mass is known as the mass defect, and is essentially the equivalent mass of the binding energy. In any nucleus there is some binding energy, the energy you would need to put in to split the nucleus into individual protons and neutrons. In a typical nucleus the binding energy is measured in MeV, considerably larger than the few eV associated with the binding energy of electrons in the atom.
Many nuclei are radioactive.
This means they are unstable, and will eventually decay by emitting a particle, transforming the nucleus into another nucleus, or into a lower energy state. A chain of decays takes place until a stable nucleus is reached. During radioactive decay, principles of conservation apply. There are three common types of radioactive decay, alpha, beta, and gamma. The difference between them is the particle emitted by the nucleus during the decay process.