the question is: an unknown substance has a vol. of 20ft^3 and weighs 3370 lb. What is the weight density?
I took 20ft^3 and converted it to 6.096m^3 and converted 3370 lb mass to 15165 Neutons so taking that divided by 6.096 m^3 I got 2,488 N/m^3. Is this correct.
Conversions 1 lb= 4.5 N and 1 ft. = .3048 m
You can get the weight density in lb/ft^3 directly by dividing 3370 by 20. That would give you 168.5 lb/ft^3. The density of water in the same units is 62.4 lb/ft^3. Therefore the specific gravity (or mass density in g/cm^3) is 168.5/62.4 = 2.70. In kg/m^3 it is 2.7*10^3. In N/m^3 it is 26,460.
The conversion factor for lb to N is 4.45, not 4.5. You also missed a decimal point somewhere.