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
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
Tarentum Taken by Hannibal
The year 542 was more unfavourable for the Romans in consequence of fresh political and military errors, of which Hannibal did not fail to take advantage. The connections which Hannibal maintained in the towns of Magna Graecia had led to no serious result; save that the hostages from Tarentum and Thurii, who were kept at Rome, were induced by his emissaries to make a foolhardy attempt at escape, in which they were speedily recaptured by the Roman posts.
But the injudicious spirit of revenge displayed by the Romans was of more service to Hannibal than his intrigues; the execution of all the hostages who had sought to escape deprived them of a valuable pledge, and the exasperated Greeks thenceforth meditated how they might open their gates to Hannibal. Tarentum was actually occupied by the Carthaginians in consequence of an understanding with the citizens and of the negligence of the Roman commandant; with difficulty the Roman garrison maintained itself in the citadel.
The example of Tarentum was followed by Heraclea, Thurii, and Metapontum, from which town the garrison had to be withdrawn in order to save the Tarentine Acropolis. These successes so greatly increased the risk of a Macedonian landing, that Rome felt herself compelled to direct renewed attention and renewed exertions to the Greek war, which had been almost totally neglected; and fortunately the capture of Syracuse and the favourable state of the Spanish war enabled her to do so.
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Reference address : https://www.ellopos.net/elpenor/rome/3-06-war-hannibal-cannae-zama.asp?pg=54