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
Measures against Sulla
The government did not fail to issue decrees against the oligarchic proconsul. Sulla was deprived by the comitia of his command and of his other honours and dignities and outlawed, as was also the case with Metellus, Appius Claudius, and other refugees of note; his house in Rome was razed, his country estates were laid waste. But such proceedings did not settle the matter. Had Gaius Marius lived longer, he would doubtless have marched in person against Sulla to those fields whither the fevered visions of his death-bed drew him; the measures which the government took after his death have been stated already. Lucius Valerius Flaccus the younger,(10) who after Marius' death was invested with the consulship and the command in the east (668), was neither soldier nor officer; Gaius Fimbria who accompanied him was not without ability, but insubordinate; the army assigned to them was even in numbers three times weaker than the army of Sulla.
10. Lucius Valerius Flaccus, whom the Fasti name as consul in 668, was not the consul of 654, but a younger man of the same name, perhaps son of the preceding. For, first, the law which prohibited re-election to the consulship remained legally in full force from c. 603 (IV. II. Attempts at Reform) to 673, and it is not probable that what was done in the case of Scipio Aemilianus and Marius was done also for Flaccus. Secondly, there is no mention anywhere, when either Flaccus is named, of a double consulship, not even where it was necessary as in Cic. pro Flacc. 32, 77.
Thirdly, the Lucius Valerius Flaccus who was active in Rome in 669 as -princeps senatus- and consequently of consular rank (Liv. 83), cannot have been the consul of 668, for the latter had already at that time departed for Asia and was probably already dead. The consul of 654, censor in 657, is the person whom Cicero (ad Att. viii. 3, 6) mentions among the consulars present in Rome in 667; he was in 669 beyond doubt the oldest of the old censors living and thus fitted to be -princeps senatus-; he was also the -interrex- and the -magister equitum- of 672. On the other hand, the consul of 668, who Perished at Nicomedia (p. 47), was the father of the Lucius Flaccus defended by Cicero (pro Flacc. 25, 61, comp. 23, 55. 32, 77).
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Reference address : https://www.ellopos.net/elpenor/rome/4-09-cinna-sulla.asp?pg=25