how to put it
I want to express that there are 16 packaging boxes which are grouped into 10 types, can I write in an e-mial " all these following 16 boxes in 10 types are now under processing."

Question

how to put it
I want to express that there are 16 packaging boxes which are grouped into 10 types, can I write  in an e-mial " all these following 16 boxes in 10 types are now under processing."

Answer

Your context is unclear.  If the boxes are in processing, then the listener and I (the speaker) am not looking at them.  If I am not looking at them, then why do I need to mention that they have been divided into 10 groups?  It is irrelevant to the goal of the sentence, which seems to be to answer the question, "What is the status of the 16 boxes?"

I would say:
     Those 16 boxes, divided by type, are in processing.

However, if you wish to include that information, I would say:
     Those 16 boxes were divided by type into 10 different groups and are now in processing.

Answer

All the following 16 boxes in 10 different types of boxes are now in progress