Voltage divider Vout not powering ESP8266
Practically speaking, you cannot create a lower voltage power rail from a higher voltage power rail using a simple voltage divider.  Not unless the current draw of the lower power rail is very small.  It's an impedance issue.  If you consider the device you are trying to power as a small value resistor relative to the resistors in your divider this will make sense, as it would be in parallel with the lower resistor of your divider essentially making it a much lower value... and no, don't go down the path of trying to make the resistor values in your divider smaller, you're trying to solve the problem the wrong way.

This is typically done using a voltage regulator to convert your 12V down to 6V.  Voltage regulators are made to do the voltage conversion and have low output impedance (i.e. they can source more current without issue).  Find a voltage regulator that will take your 12V and give you 6V and that is rated to supply whatever current you need.

Edit: Since what you really need is 3.3V, and since you potentially need a couple hundred mA of current, look at something like this: https://www.digikey.com/product-detail/en/cui-inc/VXO7803-500/102-4248-ND/7350287.  All you need to do is add a 10uF input capacitor and a 22uF output capacitor as explained in its datasheet.  That's about as simple as you are going to get.  And if you hooked up 12V to your ESP8622 already, you probably damaged it, so you will most likely want to get a new one of those too.