“Types” refers to distinct silhouettes—i.e., outline shape $+$ edge character (smooth vs serrated vs lobed). Size, angle, and rotation do not create new types. The drawing contains eight unmistakably different outlines; below is a precise taxonomy you can use to sort them.
[6pt]
Step 1: Define the shape features
Outline family (overall contour): ovate/elliptic, lanceolate (long taper), cordate (heart-shaped),
spatulate (wide end, narrow stem), rounded, etc.
Margin (edge): entire/smooth, serrate/toothed, lobed with shallow sinuses, deeply lobed.
Apex/base (tips): acute/rounded; base cordate/attenuate.
Step 2: Group identical silhouettes
Working around the page and ignoring orientation, the leaves sort into these eight silhouette classes (examples of each class appear multiple times in the drawing):
Smooth ovate — plump, egg-shaped outline with a smooth margin and an acute tip.
Serrate ovate — same general ovate body but with small, uniform teeth around the edge.
Long lanceolate serrate — narrow, elongated “spear” with many teeth along both sides.
Tri-lobed rounded — three broad rounded lobes (central lobe largest), shallow sinuses.
Deeply lobed (oak-like) — multiple rounded lobes with deep cuts, giving a “wavy” profile.
Cordate (heart) — clear notch at the base and a rounded body tapering to a tip.
Spatulate/teardrop — very wide at the distal end, narrowing into a short neck at the base.
Rounded/clover-like — nearly circular body formed by a few soft lobes, smooth margin.
Step 3: Sanity check
Verify that every leaf in the picture matches exactly one of the eight silhouettes above and that no additional, qualitatively new outline appears. This establishes the total number of distinct types as \(\boxed{8}\).