That would be a painting approximately 200 x 300 / 2.54 pixels wide by 100 x 300 / 2.54 pixels tall.
23,600 x 11,800 approx.
At best case, assuming you dont use any stencils or rulers, and have only one layer (I'll assume the layer is going to be entirely filled with paint) you'd need around 10GB of RAM. ArtRage is a 32 bit application, and can't support more than 4GB at best case, so you'd have to break your painting into 3 pieces to do.
You should question why you want 300 DPI on a painting 2 metres long. 300DPI is generally used for printed matter that is expected to be read from a distance of 300mm or so. Eg. magazines, printed A4 stuff you can hold in your hand.
Someone viewing a 2 metre canvas is going to be standing much further away and isn't going to resolve detail at 300DPI anyway. So you probably only want 75 DPI.
In that case you're looking at around 500MB or so.
AndyRage's mantra for graphics engine code:
"Sure - how hard can it be?"