Dear Krisna,

please calculate the structure factor of your lattice and look at the h, k, l dependence.

If it is equal to zero at specific h, k, l values  you have got your extinction rule.

Please see for example the attached first link (ppt a in pdf format) starting from page 292.

At the second link please have a look at the section 'structure factor calculation'. (please wait a little bit; ppt loading may take some moments).

Or google for 'structure factor calculation' or similar buzz words.

Good luck.

https://www.chem.uci.edu/~lawm/263%204.pdf

https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwisroqQ5prUAhUDQBQKHRPWD7kQFggpMAA&url=http%3A%2F%2Fhome.iitk.ac.in%2F~anandh%2FE-book%2Fstructure_factor_calculations.ppt&usg=AFQjCNGL2P_36e7GzP_rfgNz8dlLKqrwvw&cad=rja

Dear Professor Martens,

Thank you very much for your attention. I have calculated the structure factor for my crystal (simple FCC crystal). Unfortunately, I have some difficulty in understanding the next step. So I just stuck on the same step for many days.

I attached my structure factor calculation here.

Hopefully you and/or other experties have a heart to make me understand.

Thank you. 

Dear Krisna,

please have a look  the calculation for FCC lattice at the section "2.3 Examples of Fhkl in 3-D" in the attached link.

It is similar to yours but here the net h, k, l remain, from which the extinction rule(s) can be derived. 

In going from the second to the third row of your equations you lost your h, k, l values.  You have calculated the special case for h=k=l=1 at that step. When you still keep (retain)  the h, k, l expressions you will end up with the right formula, such as it is done  in the attached link.

Best regards

https://en.wikipedia.org/wiki/Structure_factor