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
Jugurtha summarily rejected both demands, and the envoys hastily returned home--like boys, as they were--to report to the fathers of the city. The fathers listened to the report, and allowed their countrymen in Cirta just to fight on as long as they pleased. It was not till, in the fifth month of the siege, a messenger of Adherbal stole through the entrenchments of the enemy and a letter of the king full of the most urgent entreaties reached the senate, that the latter roused itself and actually adopted a resolution--not to declare war as the minority demanded but to send a new embassy--an embassy, however, headed by Marcus Scaurus, the great conqueror of the Taurisci and the freedmen, the imposing hero of the aristocracy, whose mere appearance would suffice to bring the refractory king to a different mind.
In fact Jugurtha appeared, as he was bidden, at Utica to discuss the matter with Scaurus; endless debates were held; when at length the conference was concluded, not the slightest result had been obtained. The embassy returned to Rome without having declared war, and the king went off again to the siege of Cirta. Adherbal found himself reduced to extremities and despaired of Roman support; the Italians in Cirta moreover, weary of the siege and firmly relying for their own safety on the terror of the Roman name, urged a surrender. So the town capitulated. Jugurtha ordered his adopted brother to be executed amid cruel tortures, and all the adult male population of the town, Africans as well as Italians, to be put to the sword (642).
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Reference address : https://www.ellopos.net/elpenor/rome/4-04-rule-restoration.asp?pg=33