DC-DC converter from 5 V input to 6 V with an output current of about 3 A
You cannot do what you wish with a 7806 this is a linear voltage regulator that requires an input voltage a couple of volts higher than the intended output.

You need to use a boost dc-dc converter. These are widely available pre-built or if you want to build your own several ic manufacturers have online tools where you can enter your supplies parameters and they will produce a design for you (e.g. Texas Instruments webench).