The free-energy change for the formation of a protein from the individual amino acids is positive and is thus an endergonic reaction. how, then, do cells accomplish this process?

An endergonic reaction, like photosynthesis, refers to a reaction, which needs the energy to be driven. The activation energy for the reaction is usually greater in comparison to the entire energy of the exergonic reaction. The endergonic reactions are non-spontaneous.  

In the given case, in order to accomplish the process, the coupling of the endergonic reaction, that is, thermodynamically unstable reaction with an exergonic, that is, the thermodynamically stable reaction is done so that the entire free-energy change of the coupled reactions becomes negative.  

is this for the e2020 class