Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
The head of the Roman column, formed of
6000 infantry, cut their way through the infantry of the enemy, and
proved once more the irresistible might of the legions; but, cut off
from the rest of the army and without knowledge of its fate, they
marched on at random, were surrounded on the following day, on a
hill which they had occupied, by a corps of Carthaginian cavalry,
and--as the capitulation, which promised them a free retreat, was
rejected by Hannibal--were all treated as prisoners of war. 15,000
Romans had fallen, and as many were captured; in other words, the
army was annihilated. The slight Carthaginian loss--1500 men--again
fell mainly upon the Gauls.(3)
3. The date of the battle, 23rd June according to the uncorrected
calendar, must, according to the rectified calendar, fall somewhere
in April, since Quintus Fabius resigned his dictatorship, after six
months, in the middle of autumn (Lav. xxii. 31, 7; 32, i), and must
therefore have entered upon it about the beginning of May. The
confusion of the calendar (p. 117) in Rome was even at this period
very great.