Two atoms far apart being brought closer to each other, their potential energy decreases until the nuclei repel each other (the repulsion). The nucleus of one atom is attracted to the electrons of the other atom. As the distance gets less, the potential energy gets less.
Protonation means addition of proton to a compound. Protonation of NH₃ can take place if any acidic compound releases proton (H⁺ ion) easily. The acid which can be dissociated easily can donate proton to other compound. Whether the removal of proton is possible or not can be understood from its dissociation constant value (Kₐ). If Kₐ value is more dissociation of the compound is easy means H⁺ ion can be removed easily. Also, if Kₐ value is inversely related to value. If value is less, then kₐ value is more which indicates dissociation is also more, donation of proton is also easy. As per given information, value of CH₃COOH is less as compared to CH₃CH₃ and NH₃. So, CH₃COOH can protonate NH₃.