Will this circuit be able to power a 12V DC motor
There appears to be several problems with your schematic.
I assume that the only states that exist are:


Q3 ON and Q4 OFF
Q4 ON and Q3 OFF
Q3 OFF and Q4 OFF


Now the problems:


If Q3 AND Q4 are ever ON, then Q1 and Q2 will both turn on shorting your supply (large current flow). You show no understanding of the need to handle this. Normally you WOULD support Q3 AND Q4 = ON to get motor braking, with this configuration you cannot do this. 
The 1N750 has a leakage current in the 5-50uA range, far too high for the R8,R9 values you have.
The junction of R8,R9 would have values of about 0v, 6V or 12V for the states shown above. I'm not sure it is providing any viable information.


There are many H-bridge chips available, is there some compelling reason you want to implement it in the manner you have shown? You don't give any idea what the power level is of your DC motor but implementing with transistors that have significant VCE(sat) will impact driving the motor.