Io should be known by knowing first the equivalent DC resistance (R_load) of the load:
Io = 6 / R_load
BQ1 is the ratio Ic_q1 / Ib_q1
At high currents, we can approximately say:
Ic_q1 = Io
Unfortunately BQ1 is not constant. It decreases quickly near saturation (Vce < 1V for example) and at high currents.
Practically, we assume BQ1 as an intermediate value, says 50, and we let Vce_min not less than 1.5 V.
For the supply to be reliable, Vin_max should not be exceeded at the input and it is calculated from the dissipated power of Q1, then checked for the dissipiated power of LM7806.
Pmax_q1 = Io * ( Vin_max - Vout ) + Ib_q1 * Vbe_q1
Vin_max could be known if Pmax_q1, Io, Vout, Ib_q1 and Vbe_q1 are estimated based on the whole circuit board.
Pmax_q1 is related to the heatsink of Q1.
Io, as we saw, depends on the maximum load.
Vout is 6V here.
Ib_q1 is approximately equals to Io/BQ1 hence Io/50.
Vbe_q1 varies a little with the current Ib_q1 (from 0.75 to 1 V). It could be assumed as 0.9 V.
After calculating Vin_max, it is better to check the dissipation power of LM7806:
Pmax_reg = ( Ib_q1 + Vbe_q1 / R1 ) * ( Vin_max - Vbe_q1 - Vout )
Here another value is added (R1). The resistance of R1 is not critical as long Pmax_reg is within limit (also depends on LM7806 heatsink, if needed).
Usually I start with R1=33R. If I find out that, for the actual Vin_max, Pmax_reg is relatively low I can decrease R1.
Please note that designing a circuit properly is possible only when the external parts connected to it are well known. Otherwise we have to estimate and approximate
Therefore if you notice a step on the above analysis being not logical to you, please don't hesitate to point it out. You know... I may do a silly mistake anytime