How did the connubio help Camillo Benso, count di Cavour become prime minister in 1852?

The connubio (or "marriage") was a strategic political alliance between the center-right and center-left factions in the Piedmontese parliament, engineered by Camillo Benso, count di Cavour.12

By uniting these moderate forces, Cavour created a new, stable majority that possessed the parliamentary strength necessary to pursue a policy of modernization and secularization. This alliance effectively undermined the standing of the incumbent prime minister, Massimo d’Azeglio, whose government had struggled to maintain control of the chamber.21

Following the collapse of d’Azeglio’s cabinet—precipitated by the king’s refusal to support further anticlerical legislation—Cavour emerged as the logical successor. Because he was more amenable to the king's position on certain issues while simultaneously holding the support of the connubio, he secured effective control of the chamber. Consequently, Victor Emmanuel II entrusted Cavour with the formation of a government, and he officially became prime minister on November 4, 1852.12