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
They began with a regular attack; machines were erected, and in a short time the batteries had demolished six of the towers flanking the walls, so that the breach soon appeared to be practicable. But the able Carthaginian commander Himilco parried this assault by giving orders for the erection of a second wall behind the breach. An attempt of the Romans to enter into an understanding with the garrison was likewise frustrated in proper time.
And, after a first sally made for the purpose of burning the Roman set of machines had been repulsed, the Carthaginians succeeded during a stormy night in effecting their object. Upon this the Romans abandoned their preparations for an assault, and contented themselves with blockading the walls by land and water. The prospect of success in this way was indeed very remote, so long as they were unable wholly to preclude the entrance of the enemy's vessels; and the army of the besiegers was in a condition not much better than that of the besieged in the city, because their supplies were frequently cut off by the numerous and bold light cavalry of the Carthaginians, and their ranks began to be thinned by the diseases indigenous to that unwholesome region.
The capture of Lilybaeum, however, was of sufficient importance to induce a patient perseverance in the laborious task, which promised to be crowned in time with the desired success.
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Reference address : https://www.ellopos.net/elpenor/rome/3-02-war-rome-carthage-sicily.asp?pg=41