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
With the four new legions and a corresponding contingent of Italians which they brought up, the Roman army rose to 80,000 infantry, half burgesses, half allies, and 6000 cavalry, of whom one-third were burgesses and two-thirds allies; whereas Hannibal's army numbered 10,000 cavalry, but only about 40,000 infantry. Hannibal wished nothing so much as a battle, not merely for the general reasons which we have explained above, but specially because the wide Apulian plain allowed him to develop the whole superiority of his cavalry, and because the providing supplies for his numerous army would soon, in spite of that excellent cavalry, be rendered very difficult by the proximity of an enemy twice as strong and resting on a chain of fortresses.
The leaders of the Roman forces also had, as we have said, made up their minds on the general question of giving battle, and approached the enemy with that view; but the more sagacious of them saw the position of Hannibal, and were disposed accordingly to wait in the first instance and simply to station themselves in the vicinity of the enemy, so as to compel him to retire and accept battle on a ground less favourable to him. Hannibal encamped at Cannae on the right bank of the Aufidus.
Paullus pitched his camp on both banks of the stream, so that the main force came to be stationed on the left bank, but a strong corps took up a position on the right immediately opposite to the enemy, in order to impede his supplies and perhaps also to threaten Cannae.
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Reference address : https://www.ellopos.net/elpenor/rome/3-05-war-hannibal-cannae.asp?pg=33