I've been stuck on a homework problem for a long time now. I've been asked to implement a PID with TF G =\[ 6(s+1.4)^2/s \] using two non inverting op amps, no more than 4 resistors and two capacitors. My attempt is attached below. Please assist.

 

Well, there is a small error in your transfer function: The denominator is sR2C2 (and not sR2C1).
When you do some mathematical manipulation with the transfer function you can split it up into three parts: showing the P-I-D portions):

P + 1/sT1 + sT2.

 

As an alternative, you could use a simple non.inv. PI and a corresponding non-inv. PD block in parallel.
Both outputs can be superimposed using two identical resistors. However, the resulting output is not a low-resistive voltage source. But this is not required in your task description.