I believe the desired answer is the Battle of Perryville.
This question was unusual in that the source that could be used to find the correct answer was actually identified in the question.
I was able to access the book "100 Great Battles of the Rebellion" (which was published in 1906) through a Google book search. It lists battles in alphabetical order, with detailed information about casualties suffered by each regiment.
After slogging through the details, I noted that occasionally little charts labeled "Battles Compared" appear in the text. Such a chart appears on pages 128-129, showing numbers of regiments and men killed per regiment at Gettysburg and Fredericksburg that match the figures quoted in the question. That same chart indicates 48 regiments, with an average of 19 killed per regiment, at Perryville. I presume that this or a similar chart was the basis for the question that was asked.
I have a feeling, although it is not explicitly stated either in the book or in the question that was asked, that the charts relate strictly to the number of Union regiments present and Union soldiers killed at the indicated battles. I don't think they represent the combined total number of regiments and soldiers killed, including both Union and Confederate.
I also note that the person who prepared the chart on pages 128-129 apparently overlooked the fact that the summary for the Battle of Perryville, which appears on pages 192-193, indicates only 47, rather than 48, regiments were involved with an average of 18, rather than 19, killed per regiment.