Confused about a problem

[badal.03062000]

I have G41mt-s2 motherboard does it support the 4gb Graphic cards?

 

[Slow Pri]

Yeah the Gigabyte G41MT-S2 supports 1x PCI Slot x16. Any GPU you put in that has 2GB, 4GB, 6GB vram will work.

 

[Barty1884]

The VRAM of a GPU is not the deciding factor.

That's an older board, supporting up to Core2Quad CPUs..... so I'd suggest no higher than the 700 series from nVidia - as some older boards can occassionally have issues with newer (900 or 10 series) GPUs. Chances are, that board would support any modern GPU you wanted to run though.

That being said, consider what CPU you're pairing it with. The strongest CPU supported by that board is a QX9770 which is almost 10 years old.
https://ark.intel.com/products/34444/Intel-Core2-Extreme-Processor-QX9770-12M-Cache-3_20-GHz-1600-MHz-FSB

I wouldn't look to pair anything greater than a 750TI/1050..... maybe a GTX 1050TI at a stretch, but the CPU is going to be a limiting factor by then (depending on your use case, of course).