This is something you can easily do in Workbench LS-DYNA:
In LS-PrePost, you can check the element quality as follows:
Note that you will have different mesh quality metrics based on the element type (solid or shell) selected.
You can count the number of hex elements vs tet elements by looking at the element formulation (elform):
Solid elform=1 are hex elements while solid elform=10 are tet elements.
You can get the number of solid vs shell elements in LS-PrePost by clicking Misc. > View Model Info:
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