7812 minimum input voltage?
A 7812 is a linear regulator, and does not step up the input voltage if the input is below the output (for that you need a DC-DC boost regulator).  The input voltage must be above the output.  All linear regulators have a minimum dropout voltage, or difference.

The 7812 is not a LDO (low-dropout regulator), as the typical dropout voltage is around 2 volts.  (An LDO might have a dropout voltage of 0.7 volts).

On page 6 of the datasheet, the maximum dropout voltage Vd is listed as 2.5 volts, meaning you need a minimum of 14.5 volts input to the device to guarantee an output of 12 volts..