Final answer:
While detailed records of the persuasion by Bishop Valerius of Bishop Megalius are scarce, Augustine's leadership against heresies and his role at the 411 Council of Carthage highlight the qualities that likely influenced Valerius to advocate for Augustine's consecration as bishop of Hippo.
Step-by-step explanation:
The question pertains to how Bishop Valerius was able to convince Bishop Megalius to consecrate Augustine as a bishop of Hippo. Historical records, including those related to Augustine's debates and writings against heresies such as Donatism and Pelagianism, suggest Augustine's intellectual prowess and theological stance may have played significant roles in his elevation to the episcopate. The details around the actual act of persuasion by Valerius on Megalius are not extensively documented, leaving it to the realm of academic inference based on Augustine's well-known activities and his role at the 411 Council of Carthage.
Augustine's defense of theological orthodoxy against various heresies and his leadership at the Council of Carthage, which dealt a fatal blow to Donatism, signal his importance in shaping early Christian theology and church policy. Augustine's opposition against competing religious thoughts, as well as his active participation in ecclesiastical and philosophical discourse, demonstrate his capability and the probable trust that Valerius held in Augustine's ability to shepherd the Christian community in Hippo effectively.