Transient response of a step RL circuit
Your mistake is here: this equation you say is correct: 

v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ), 

but note there is v(0+), not V(0-) = 6 V you are using, and get the wrong result: 

v(t) = [6]e^(−t/τ) 

The voltage immediately after closing the switch is 4 V, and by placing it to the equation you get the right result:

v(t) = v(∞) + [v(0+) − v(∞)]e^(−t/τ) = 0 V + (4V - 0V)e^(−t/τ)=4Ve^(−t/τ)