Does my motherboard support 32GB of RAM?

Yes, it almost certainly does. Unless you’re running something ancient like a Core 2 Duo from 2009, 32GB isn’t exotic anymore. DDR4 and DDR5 boards from the last six or seven years typically support 32GB easily, often much more. Check your motherboard’s spec page and CPU’s memory support, but two 16GB sticks will work in almost any modern consumer board.