It is true that the mass of both protons and neutrons is greater than 1 amu - when treated as separate items.
However when they are combined together into a nucleus some of the mass is converted into energy according to Einsteins E=mc^2 - This is called the nuclear binding energy and the missing mass is called the mass defect.
It is the principle behind nuclear fusion energy. Small nuclei bind together and release energy - this energy is directly converted from the mass lost.
In a hydrogen bomb the small nuclei of the deuterium with one proton an one neutron are forced together to form one helium atomic nucleus. The mass lost is turned into energy and the reaction releases this energy as a sudden blast of radiation and heat.
These nuclear reactions are nothing to do with chemical reactions and are the only examples of the non-adherence to the law of conservation of matter.
In reality chemical reactions that release energy must also cause a mass difference but as this is so tiny as to be unrecordable then we say that mass is conserved.
To go back to carbon nuclei - if the nucleus is measured (=12amu) and the sum of 6p and 6n is added up, the difference is due to the nuclear binding energy. If you wished to separate the nucleus into its individual nucleons then this quantity of energy would have to be absorbed and would turn into the mass required for the total of 6p + 6n.
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