Why are these electric circuit transformations giving me different answers? (See details)
Your error is with the wire on the far left, the one that is bent, in parallel with the 4Ω.  I assume you forgot that that wire removes the 4Ω resistor by shorting it. 

So if you short the 4Ω resistor on the far left (as you should), then you get $$8Ω || 4Ω || 1Ω = \frac{8}{11}Ω$$