Calculating resistor's value to use it with a LED
So if I use the formula diferently: 6v/150ohm = 0.04a.


In the above, you're evidently assuming that there is 6V across the 150 ohm resistor.  Remember that Ohm's law relates the voltage across and current through the resistor:

$$v_R = R \cdot i_R$$

So, if you want to solve for the current through the resistor, you divide the voltage across the resistor by the resistance.

Since you have a 6V battery and since there is about 3V across the LED over a wide range of current, you can approximate the voltage across the resistor as

$$v_R \approx 6V - 3V$$

Then, to correctly apply Ohm's law, write:

$$v_R = 3V = R \cdot i_R $$