In photoshop when I try to select and delete the area of image it sometime white but I want transparent. What is the solution ?

Delete selection gives you color in2 cases, if you are on "Indexed Color Mode" or you are editing the background layer.

just double click layer to convert it to a normal layer and delete, and for mode go to >Image>Mode>RGB/CMYK

First of all, select the area with Lasso tool or any other selection tool. If you want reverse selection you can press "Ctrl+Shift+I". Now press "Delete" button from keyboard. Make sure your layer should be unlock. 

May be it due to the lock layer. To unlock, double click on layer and press "OK".

Hope it will help.

you can use tool select to area and make copy to the part which want to delete it