One quantum of energy I came across a question that asked me to identify which transition within a hydrogen like atom will result in the emission of one quantum of energy. Exactly what is the definition of "one quantum of energy"? Does such a definition even exist? 
 A: From your comments, I note that the following additional information applies :

The options are as follows:
  $a. 4\to 2$
  $b. 2\to 1$
  $c. 3\to 1$
  $d. 4\to 1$
  And according to the answer key, all the options are correct! 

I presume these numbers relate to the principal quantum number $n$ which identifies the energy levels of an isolated hydrogen atom. There are additional subordinate quantum numbers for each value of $n$. As @lemon points out, selection rules restrict which transitions can result in the absorption or emission of a photon. However, such transitions are always possible between any 2 states with a different principal quantum number $n$.
So for each option the transition can result in the emission of a single photon. At your level of study, absorption or emission will occur only 1 photon at a time, and you are correct in making this assumption. So as you note from the answer, all options are correct.
Perhaps where you are getting confused is that 2 or more consecutive transitions are also possible, with some delay in between : eg $4\to 3\to 2\to 1$ with the emission of 3 photons, each with different energies.
The largest release of energy is usually the most likely - provided that other quantum numbers can change according to the selection rules. So for a hydrogen atom excited to the $n=4$ level the transition $4\to 1$ is most likely, with the emission of a single photon. But nothing prevents the transitions $4\to 2$ or $4\to 3$ instead, with later transitions $2\to 1$ or $3\to 1$ or $3\to 2\to 1$ eventually leading down to the $n=1$ level, with the emission of more photons - again 1 for each transition. These are much less likely but not impossible, and represent a small proportion of the transitions which do occur.
