How the second transistor from the left reaches the ON state.
After all, there is no closing of a circuit from the positive voltage of the voltage source, the current can not reach the negative voltage source, because it is stopped at the collector of the first transistor from the left,
YOU CAN SEE FROM THE schematic THAT THE TRANSISTOR A IN THE BOTTOM WILL NOT CLOSE A CIRCUIT IF YOU ATTACH A VOLTTAGE IN THE BASE
BECAUSE THE COLLECTOR OF TRANSISTOR B WILL STOP THE CORRENT TO GET TO THE GROUND,
WHENEVER TRANSSTOR B IS OFF.
IF THE CURRENT THAT YOU ATACH ON THE BASE OF TRASISTOR A IN THE BOTTOM CAN NOT REACH THE GROUND, THAN IT WILL NOT EXIT FROM THE POSITIVE VOLTAGE SOURCE AT ALL.
It's a two transistor "AND" gate circuit - if BOTH are turned on, the two in series pull the upper collector voltage down to a low level; that forms a "NAND" (NOT AND) gate.
The next transistor across inverts the output, so its collector goes high when both the first bases are driven, so the output at that point is AND.
The two on the right form an OR (or rather NOR) gate, but that is only enabled when the AND gate output is low.
Either input alone activates the OR stage; but both together disable it, so the overall function is XNOR, Exclusive NOR.