If you RMB on Mesh you can select Generate Mesh and you will get unstructured tetrahedral elements. With Mesh selected, the Details window allows you to set a global element size.
You can apply mesh controls to bodies such as Hex Dominant meshing which will try to use Hex elements but mix in Tets where it must.
For a fully structured mesh of hex elements, the solid bodies must be sliced in DesignModeler into six sided sweepable bodies and put into one multibody part where the bodies can use Shared Topology to have shared nodes on coincident faces.
I see that you could put two planes through the long axis of the box to just mesh 1/4 of the geometry. Try Unfreeze on all bodies so you can use the Slice with a Plane method I outlines before.
Save your project, then in Workbench, File > Archive, to create a Workbench Project archive .wbpz file that you can attach to your post, making it available for me and anyone to download and reply with meshing suggestions for you to use. Be sure to say what version of ANSYS you are using. It looks like V14.5 Is there a chance that you can upgrade to the latest version?