Can someone help me find the initial condition on this circuit for i(0)?

 

Sure, but what's the fun in that?

So, let's look at the problem... Before t=0, the switch is open, meaning the two resistors are a part of the circuit. We assume a steady state condition before t=0, so, what does an inductor act like at steady state when frequency = 0?

An inductor acts as a short at steady state with a DC source, so the voltage across the inductor = 0 @ t < 0, so the current through the inductor is governed by the resistors. We know that the current through an inductor cannot change instantaneously, so the current through the inductor at t<0 is the current through the inductor at t = 0.

 

so the i(0) for this circuit will be :
i(0)=6/(2+1) ?

 

6/(2+1) what? Amps? Megacoulombs? Ducks?

If I tell you that a building is 300 tall, is it closer to 2 stories, 20 stories, or 60 stores (or something else entirely)?

Units count!

Your answer should be

i(0+) = i(0-) = 6V/(2Ω+1Ω) = 2A