The coenzyme that carries high-energy hydrogens during the process of respiration is NADH (nicotinamide adenine dinucleotide) and FADH2 (flavin adenine dinucleotide).

Here's a breakdown:

* NADH: During glycolysis and the Krebs cycle, NAD+ accepts two electrons and a proton (H+) to become NADH. This NADH carries high-energy electrons and a proton to the electron transport chain where they are used to generate ATP.

* FADH2: Similar to NAD+, FAD (flavin adenine dinucleotide) accepts two electrons and two protons to become FADH2. FADH2 also carries high-energy electrons to the electron transport chain.

Both NADH and FADH2 are essential for the efficient production of ATP in cellular respiration. They act as electron carriers, transferring the energy stored in high-energy electrons to drive the process of oxidative phosphorylation.