I'm trying to complete this circuit (see attachment). LED should turn on when input is less than 8 or greater than 12.

 

What specifically do you want to know? If this is a homework question then it's really better off in the "Homework Help" board. People aren't going to be willing to answer your question if you don't provide any input yourself. Everyone who posts here does it to help others and learn from others... not just to get answers. Show a little more willing or at least an attempt at the question and you might get some help.

 

First start with the led. What logic level do you need for it to turn on?
Then the NOR gate - what input you need to get that output logic level?
Then the comparators, what number do you need to compare with to get those outputs?

 

I'm trying to complete this circuit (see attachment). LED should turn on when input is less than 8 or greater than 12.

Good luck! Let us know how it works out.

 

I want to know how to connect the inputs for this circuit to operate properly I've made several attempts at it with no success.

 

Check that you have DC power to each chip, a common error because + and - power are not normally shown on the schematic, it is assumed that power is supplied to the appropriate pins of each chip, only the logical inputs and outputs are shown. Look up the Datasheets for each chip on google.com for the appropriate pin assignments.

Then, take a nice photo of your project so we can help with wiring errors and give more advice.

Good luck.