You have two options to drive from Belize City to Placencia:
Option 1: shortest drive via the Western Highway, then the Coastal Highway, the Hummingbird Highway. Unfortunately, the Coastal Highway is a compacted dirt road with large potholes and it can get very muddy when it rains.
Option 2: most convenient drive via the paved Western Highway all the way to Belmopan and then change to the paved Hummingbird Highway and after Hope Creek you will then take the paved Southern Highway
More information can be found here: https://backpackandsnorkel.com/Belize/Placencia/#DriveToPlacencia