Why was the mass of carbon assigned the value of 12 in relative atomic mass? I mean to say, masses of all other elements are determined relative to...

The mass of all the elements is determined with respect to carbon and not hydrogen. Incidentally, for a very long time, the standard of atomic mass was oxygen and not carbon. This was due to wide-spread presence of oxygen-based compounds at the time. However, it was later found that carbon was a more prevalent element and most of the material were based on carbon. Thus, carbon-12 was selected as the basis for determining the mass of other elements. Incidentally, the selection of carbon-12 was a compromise between chemists and physicists. The former used oxygen-16 as the average mass of all isotopes of oxygen, while the latter used 16 as the mass of pure oxygen-16 isotope. 

The atomic mass of carbon-12 can be determined using mass spectrometry. 

Hope this helps.