Ill try and explain it,
You have got one 74373 chip that controls the Green
Cathodes of the 8x8 matrix, 8 pins of the Green
74373 connects to the 8 transistors that control the 8 cathodes ROWS of GREEN Leds..
Now 1 pin from the green 74373 chip goes to a RESISTOR and then to the TRANSISTOR.. you then have another RESISTOR from the TRANSISTOR to the Cathode of one ROW of green leds..
The last pin on the TRASISTOR connects to Ground..
you then connect the other 7 pins from the Green 74373 chip to the other cathodes using the same connections as i described above..
then you do the same for the RED
so its goes (red)74373 to a resistor, then to the transistor and from the transistor to a resistor which connects to the cathode of one row of RED leds.
When connecting the Column 74373 to the 8x8 ANODE there are no resistors or transistors connected.
I hope this helps, if not then feel free to ask
But please read the DATASHEET for the type of transistor you use, so you know how to connect it up correctly, heres a picture to help.