Common Cathode Led being Switched By a transistor

I am trying to switch on a common anode LED as per the inserted diagram. Having no luck and cant see what I am doing wrong

10K is far too large for the transistor, try a 1K.

Your schematic shows common-anode LEDs. Which do you have?

If they are actually common-cathode then you need to reverse the supply voltage polarity and use PNP transistors.

Most ordinary 5mm LEDs are spec'd with a current of 20mA. The current-limiting resistor value for the RED LED is far too low:

1) A red LED is about 1.9V so when the transistor turns on and saturates with a voltage loss of 0.1V then the 270 ohm resistor limits the current to (12V - 1.9V - 0.1V)/270= 37mA which will melt a normal 5mm LED.

2) With 510 ohms the current is 19.6mA.

3) A new bright green or blue LED is about 3.5V. Then the 430 ohm resistors limit the current to 19.5mA.

Little transistors saturate well when their base current is 1/10th the collector current.
The collector current will be 19.5mA so the base current should be at least 1.95mA. (12V - 0.7V)/1.95mA= 5795 ohms. Use 5600 ohms for each base resistor.