First of all: If the onboard graphics chip is sufficient for your applications, a Mini ITX form factor would also be conceivable.

PCIe 3.0 is backwards compatible with PCIe 2.0, so you can plug one into the other.
The decisive factor is the transfer speed.

This is a "PCIe x1 interface card" (can be seen on the manufacturer's site), i.e. only one lane is used.
Maximum lane speeds:
PCIe 2 500MB/s (-20% overhead => effectively 400MB/s)
PCIe 3 985MB/s (-1.5% overhead => effective 970MB/s)

The maximum transfer rate of this card is 2400Mbp/s = 300MB/s (Megabit = 1/8 Megabyte); thus far below the maximum for PCIe 2.

The relevant information can best be found on the manufacturer's website under Specifications: Expansion Slot.
e.g. for the B450 Aorus Pro: one PCIe 3.0 + two PCIe 2.0

TL;DR: As long as the motherboard has a free PCIe 2.0 slot (or higher), it is compatible with this card.

As long as it is not a Mini ITX board, it should work. More detailed information about the board would be useful to be able to check the specifications. Check for a PCI-E 3.0 interface on your board.