If your Motherboard supports a HD6670 than it should support newer AMD GPU Card. You just need to have a PCIe x16 8 or 16 speed) slot.
First to upgrade your HD6670 you need to see if your PSU is able to supply enough power for todays newer GPU Cards (Powerful enough). Also need to know if your current PSU has the proper PCIe GPU Power cables to connect to the new GPU cards if applicable. Normally a 6 or 8 pin PSU GPU power cables.
Go to this PSU-GPU website that gives you the Minimum PSU Wattage you will need for your computer for various GPU cards as a Reference: PSU REQUIREMENTS - RealHardTechX
Also you need to know if your Computer case is large enough for todays bigger GPUs that many takes up to 2 slots on the Motherboard.
Plus how powerful your CPU or Processor you have installed. A weak processor will bottleneck a newer powerful GPU card performance.