...8m/6m wide design at 1440dpi actual size?
...sounds ridiculous to me...
...even with a higher spec computer billboards don't need to be this high a resolution at actual size, and photoshop would be a sloth to use, even unusable...
...more RAM than 256Mb would be advisable and a worthy upgrade for any machine to perform better...
...you can adequately calculate your artwork to be reproduced at 100dpi actual size, so working to scale you can have for example a PSD at 80cm x 40cm (10% actual size for the 8m x 4m) at 1000dpi...
...when output you end up with 100dpi, which for billboards is sufficient, simply because they are viewed from a great distance, probably 20 metres or more away...
...of course you till have a very large image data (around 1.39gb) even when considering output to 100dpi, so 1440dpi actual size you can see would be ludicrous and unmanageable...
...sure, you can submit it at 1440dpi, but at a scaled size, so for further example your 8m x 4m would need to be 55.56cm x 27.78cm at 1440dpi, which again means an output of 100dpi, this is about 7% scale...
...and as mentioned, the more you can keep vector format in illustrator or another vector package, the smaller your file sizes will be, but you still need to work to scale in your vector package, so it is easier to work to a rounded scale such as 10% of actual size...
...personally i would approach your print provider to ask if your target of 100dpi when output is OK, it could well be less, it is not uncommon for designs to be calculated on resolution output as low as 35dpi (or even lower), but that would be more for artwork to span the size of multi-level building, viewed from streets away...
...if they insist on 1440dpi at actual size on computer they are barking mad, or they really mean a resolution of 1440dpi at a scaled size, which is more likely...
...but even with what I have said, you need more RAM as photoshop is a beast for memory, in fact Adobe applications are all pretty memory hungry...
...as you only have 40Gb hard disk too, worst case you'll be using a good 2 to 4Gb just for the artwork if all you have is photoshop (based on 100dpi output), so make sure it is a clean and well backed up machine...
Andrew