Supermesh Analysis of circuit of two loops
Your logic is impeccable! :-)
 You just need to trust the answer and see where it leads you..

3 Choices 

The less you take from me nd the more you do yourself the more you will learn and the happier you will be afterwards. So, I have given you a progressive answer. Use as little as possible.
Check answer once youv'e got it correct. 


(1) Single clue
(2) Progressive clues
(3) Answer


(1) You can take it from me that you are correct and that 


For  

3 amps x 'X' volts to equal zero 

then X must equal zero.
So V1 must equal zero


And go away and work it out.



OR

(2) Try these few progressive clues:

Stop after each clue and think. 


If V1 = 0 then what is the current from the 18V supply?


Stop reading. Think about it.

Then clue 2 - stop reading now to avoid clue 2. 
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Clue 2:
The current from the 18V supply and the 3A current both flow into Vi.
Where do they go to?


Stop reading. Think about it.

Then clue 3 - stop reading now to avoid clue 3.
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Clue 3
For the currents in clue 2 to go where they must go, to what is the necessary voltage of Vs?


Stop reading. Think about it.

OR - answer below - Then clue 2 - stop reading now to avoid answer. 
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(3) ANSWER:


For power in current source to be zero, voltage across source must be zero. Call voltage at top of current source Vi.
So Vi = 0
If Vi=0 then 18V supply sees a load of 3+2 = 5 ohms.
Current from 18V supply is i=V/R = 18/5 = 3.6A.
Node at Vi has current from current source + current from V18 flowing into it.
So Current in = 3A + 3.6A = 6.6A.


Current into Vi MUST go somewhere.
Only path is via Vs.
Voltage across V2 + 8R + 6R = 0
For 6.6A to flow in 6+8 = 14 ohms via Vs the voltage must be V = IxR = 6.6 x 14 = 92.4V.


Required polarity to "suck' current via 14 ohms as shown is -92.4V


QED.