You need to learn about the base to emitter voltage of a turned on transistor. It is about 0.7V. The datasheet for the BC108 transistor shows that it is typically 0.7V when its collector current is about 10mA and its base current is about 0.5mA.
Then simple arithmetic is used to find the voltage across the 22k base resistor which is 9V - 0.7V= 8.3V.
Ohm's Law is used to simply calculate the base current which is 8.3V/22k ohms= 0.377mA.
But we do not know the color of the LED so we do not know its forward voltage. Assuming that it is a 1.8V red LED and assuming that the collector to emitter voltage of the turned on transistor is 0.1V then the 330 ohm resistor has a voltage across it that is (9V - 1.8V - 0.1V)= 7.1V. Ohm's law is used again to simply calculate the collector current that is 7.1V/330 ohms= 21.5mA.
Maybe it is a 3.3V blue LED. Then the 330 ohm resistor has a voltage across it that is (9V - 3.3V - 0.1V)/330 ohms= 5.6V. YOU calculate the collector current.