Amplifier Gain and Offset (Positive m and Negative b)
I don't know where you got the numbers from. Your circuit should give you (1+51.1/11.9) * 2V + 2V out with 4V applied, which is 12.59V out, and 2V out with 2V applied. You can easily run the simulation in Circuitlab if you want (flip your power supplies first, they are reversed). 

You want a gain of 5 (2V change = 10V on the output) so the resistor ratio must be 4:1. Say you use 40K and 10K. 

For offset to 0 for 2V in, note that the gain is -4 (as compared to +5) from the inverting input so you need to apply 5/4*2V = 2.5V to the 10K resistor, as shown below:







simulate this circuit &ndash; Schematic created using CircuitLab