Before a noun with a determiner (e.g. the, my, these), both and both of are both possible.

     She's eaten both (of) the chops. Both (of) these oranges are bad.

     He lost both (of) his parents when he was a child.

We often drop the or a possessive after both; of is not used in this case.

     She's eaten both chops. (NOT ... both of chops)

     He lost both parents when he was a child.