Mr. Suzuki used various arguments to talk his son out of studying abroad.
Literal
Suzuki-Mister [topic-は] in-various-ways persuading son [of-の] study-abroad plan [object-を] caused-to-stop.
やめさせる is the causative of やめる ('to stop, quit') — 'to make (someone) stop X.' The son is the implied causee (given context); the plan is the thing stopped. 説得する ('to persuade') in て-form chains into the causative 'causing to stop.' Complex multi-step action described in one smooth clause.