H-bridge: Augmenting output from an existing IC
What @Chris is saying is that your BJTs will get very warm with 6A flowing thru them because they are configured as push-pull emitter followers and, because of this, will inevitably drop about a volt across the conducting transistors. 

Now, figure out how much that electricity costs to throw away and decide which is the cheaper option - the ones you have in your box (presumably paid for) or the new transistors dissipating about 12 watts all the time the solenoid is being driven. 

Having said all of that the existing chips have a total (upper and lower) on resistance of 0.35 ohms (see page 5 of the data sheet) and, 2 of them in parallel at 6A will waste about 6.3 watts total. Get a better device is my advice and save the world.