Explanation:

To find the number of levels in the AVL tree after deleting the element '4', we need to understand the concept of AVL trees and how they are constructed.

AVL Tree:
An AVL tree is a self-balancing binary search tree. It maintains a balanced tree structure by ensuring that the heights of the left and right subtrees of any node differ by at most 1.

Insertion in an AVL Tree:
When inserting elements into an AVL tree, we follow the following steps:
1. Start with an empty AVL tree.
2. Insert the elements one by one in the order given: 7, 4, 9, 5, 4.5, 6, 5.5, 5.2.
3. After each insertion, check the balance factor of the nodes on the path from the inserted node to the root.
4. If the balance factor of any node becomes greater than 1 or less than -1, perform the appropriate rotation to rebalance the tree.
5. Repeat steps 2-4 until all elements are inserted.

Deleting an Element from an AVL Tree:
To delete an element from an AVL tree, we follow the following steps:
1. Start with the AVL tree.
2. Find the element to be deleted.
3. If the element is found, delete it using the appropriate deletion technique.
4. After deletion, check the balance factor of the nodes on the path from the deleted node to the root.
5. If the balance factor of any node becomes greater than 1 or less than -1, perform the appropriate rotation to rebalance the tree.
6. Repeat steps 2-5 until all elements are deleted.

In this case, we need to delete the element '4' from the AVL tree. After deleting '4', we need to find the number of levels in the AVL tree.

Steps:
1. Start with the AVL tree after inserting the given sequence of elements.
2. Delete the element '4' from the AVL tree.
3. After deletion, check the balance factor of the nodes on the path from the deleted node to the root.
4. Perform the appropriate rotations to rebalance the tree.
5. Repeat steps 2-4 until all elements are deleted.

Explanation:
The AVL tree after inserting the given sequence of elements will look like this:

7
/ \
5 9
/ \ \
4.5 6 10
\
5.2

After deleting the element '4' from the AVL tree, the tree will look like this:

7
/ \
5 9
/ \ \
4.5 6 10
\
5.2

The number of levels in the AVL tree is the maximum number of edges from the root to any leaf node. In this case, the maximum number of edges from the root to any leaf node is 3.

Therefore, the number of levels in the AVL tree after deleting the element '4' is 3.

Conclusion:
The correct answer is option 'C', i.e., 3.