Now for a motor, 6v or 5.8v or whatever the output will be if the input voltage goes below 8v may not matter. So the 7806 may not give you 6v if the input voltage goes under 8v, which may happen with a 9v battery or a lousy 9v power supply, especially when the diode is dropping some voltage. This voltage drop is important because linear regulators like 78 need about 2v about the output voltage to give you proper output voltage. Afrotechmods on Youtube has a video about it. To get this voltage drop lower you may want to use a schottky diodes like 1n5817-1n5819 which have an average of 0.3v 400mA, 0.6v I guess you use it as a sort of reverse voltage protection - look into using mosfet for that, you won't lose any voltage using mosfets. So you'd really have 8 - 8.2v input voltage. The reason I asked what 9v supply you have is because the 1n4004 will drop about 0.8v at 100mA and about 1v at 1A. Of course it will last for more than 1A for a few seconds of motor running, if motor uses more than 1A. If the motor uses more current, you should at least use a largeish capacitor at the input to make the battery happier (1000-2220uf/16v wouldn't hurt) 1n4004 is good for 1A max.

How much current is that motor going to pull? How good the 9v power supply is going to be? Is it the unregulated kind that will show 10-12v at low loads, under 9v when lots of current is pulled? Or are you planning to use a 9v battery? Keep in mind that 9v batteries can only provide 100-200mAh reliably.

Fritzing 9v power supply