Correct : 11

A full binary tree requires every node to have exactly 0 or 2 children. With 23 nodes, the number of internal nodes = (23−1)/2 = 11 and the number of leaves = (23+1)/2 = 12.
To maximise the height, we build the tree as a right-leaning skewed chain. At each level along the main path, we place one internal node whose one child is a leaf (terminating there) and whose other child continues the chain down to the next level. This uses one internal node and one leaf per level.
With 11 internal nodes, the main chain goes from level 0 to level 10, consuming 10 internal nodes and 10 leaves (one leaf per level as a sibling branch). The 11^th internal node sits at level 10 — it has no more internal node children available, so both of its children must be leaves at level 11. This accounts for the remaining 2 leaves, giving a total of 12 leaves ✓
The deepest leaf is at level 11, and since height is defined as the number of edges in the longest root-to-leaf path, the maximum height = 11.
Correct answer: 11 ✓