I suspect your student's $32$ billion year value comes from the estimated proper distance to GN-z$11$, which was discovered in $2015$, with details about it published in a $2016$ paper. In particular, the last sentence of the first paragraph in that Wikipedia article states
Up until the discovery of JADES-GS-z$13$-$0$ in $2022$ by the James Webb Space Telescope, GN-z$11$ was the oldest and most distant known galaxy yet identified in the observable universe, having a spectroscopic redshift of z = $10.957$, which corresponds to a proper distance of approximately $32$ billion light-years ($9.8$ billion parsecs).
Since a light-year is generally defined as the distance that light travels in a vacuum in a year, that would appear to, at first glance, imply the light from GN-z$11$ has been travelling for about $32$ billion years and, thus, the universe must be at least that old. However, regarding the discrepancy of this distance compared to the currently generally believed age of the universe, the next paragraph states
... It is observed as it existed $13.4$ billion years ago, just $400$ million years after the Big Bang; as a result, its distance is sometimes inappropriately reported as $13.4$ billion light-years, its light-travel distance measurement.
Also, as explained in the Comoving and proper distances Wikipedia article, the main cause of the apparent discrepancy is due to the expansion of the universe, which means the distance between the starting point and its current position is actually considerably more than what would normally be expected based on the speed of the light relative to the local region of space it's in at any particular time (thus, for GN-z$11$, this means the universe expansion has caused an about $32-13.4=18.6$ billion light-years increase in distance between where GN-z$11$ was $13.4$ billion years ago and our current position). As well, the article gives the definition
... Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. ...
Note that there are multiple posts on this site regarding the definition and use of various distance measures in cosmology, such as the proper distance, e.g., there's The difference between comoving and proper distances in defining the observable universe, Difference between physical, proper, and co-moving distances, Proper distance in cosmology, etc.