Yes, this laptop supports DDR4 at 3200MHz.
Yes, this laptop supports DDR4 at 3200MHz.
The RAM on your client's laptop is 2400MHz, but it might struggle with 3200MHz. It supports DDR4 and the i3-6006U chipset, so it should work fine with the included memory.
Here are some details about the product:
This information pertains to a compatible upgrade for the Dell Inspiron 15 (model 3567). It specifically addresses memory-related upgrades.