Calculating peak current using efficiency for switching regulator
Firstly, the equation IS NOT the formula for calculating peak inductor current, it's the equation for calculating average DC input current; just look at its structure - it doesn't contain any mention of duty cycle and duty cycle is needed to be known to calculate inductor peak current.

So, if your output power is 12 watts and your efficiency is 0.85 then input power is 14.12 watts.

If input voltage is 3.2 volts then average input current is 14.12/3.2 = 4.4118 amps.

What you appear to be proving is that 12 x 1.15 does not equal 12/0.85. Or put more simply, 1.15 does not equal 1/0.85.