It is not clear whether the question means the shape has ten faces of which 4 are square and 6 are not, or 6 faces of which 4 are square.
In the first case the shape would be a 16-hedron. The second is impossible.
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A square-based pyramid.
square based Pyramid
It is a cube.
A square pyramid has 5 faces and 5 vertices.
It is a cube that has 6 identical square faces, 12 edges and 8 vertices.