I can explain the calculation here.
EDIT: (Please note that it is a calculation in which the transistor BC337 is omitted)
Your input voltage Vdc = 13.5V
Voltage drop across a single IR LED Vled = 1.2V
Total voltage across 6 LEDs 6X1.2V = 7.2V
Now the Voltage that must be dropped across the Resistor Vr = 13.5-7.2 V = 6.3V
The current Flows through the LED I = 100 mA
The current Through the resistor is same, I = 100mA
Now the Value of resistor R = V/I = 6.3V/100mA = 63Ohm.
(Puting a standered value, R = 6.8 Ohm)
Now The Power Calculation
The power dissipated in the Resistor P = V X I = 6.3V X 100mA = 0.63W
Now you can't use ordinary 1/4W or 1/2W resistors.
It is better to use a 1W resistor of 68 Ohms.