On a Kanji exercise, I was told to find how 人口 is read.
Because the kanji are a word, I used the on-yomi of both and I answered "にんこう".
Is that correct?
No, 人口 is read じんこう (look the word up in a dictionary). Some kanji have more than one on'yomi. This is due to the fact that they were imported from different areas and/or in different eras from China.
For 人, ジン is a kan'on (漢音) reading and ニン is a goon (呉音) reading.
In compound words, usually both have the same type of on'yomi. Here, both ジン and コウ are kan'on readings. (口 also has the different jōyō reading, namely the on'yomi ク, which is a goon reading.)
You are correct in that 人口 is a word (meaning "population"), but it is pronounced じんこう. In this instance, both kanji are using on-yomi, which is commonly used in compounds that linguistically originate from Japanese rather than Chinese.
Dictionary entry from JDIC is here. You can easily find pronunciation(s) in dictionary entries. http://www.edrdg.org/jmdictdb/cgi-bin/entr.py?svc=jmdict&sid=&q=1367300