Four AA alkaline battery cells in series make 6V to 6.4V only when they are brand new and fresh.
Four AA Ni-Cad or ni-MH cells in series make about 4.8V to 5.2V when fully charged.
A white LED has a forward voltage of 3.2V to 3.6V so with a 150 ohm resistor and a 6V battery its current is from 16mA to 18.7mA.
A red LED has a forward voltage of 1.7V to 2.2V so with a 6V battery and a 400 ohm resistor its current is from only 9.5mA to 10.8mA.
The red LED needs a current-limiting resistor value of 238 ohms (use 220 ohms or 240 ohms) for a current of about 17mA.
Your calculation with a 6V battery and a 400 ohm resistor produces 15mA if the LED is a dead short.