(Carrano, p. 565-9)

Insertion — Avoid Parent Corrections

At each step of the traversal to insert, if you encounter a 4-node (n), split it.

• Let p be the parent of the 4-node.  If the 4-node is the root, create a new node p.
• Move the middle value into p.  Since p is not a 4-node, there is room for the value.
• Create a new node n1 as the leftward child from that value holding the smallest key from the 4-node.  Give n1 the two left children of n.
• Create a new node n2 as the rightward child from that value holding the largest key from the 4-node.  Give n2 the two right children of n.

Deletion — Avoid Parent Corrections

At each step of the traversal to delete (either to find the value or, for interior nodes, to find the in-order successor to replace that value), if you encounter a 2-node, amplify it to a 3-node or a 4-node:

• If an adjacent sibling is a 3-node or a 4-node, redistribute values so the the present 2-node becomes a 3-node.
• If an adjacent sibling is a 2-node, merge the two nodes:  generate a 4-node by bringing down the key value from the parent — which is know to be either a 3-node or a 4-node, and consequently can lose a key and a child without becoming illegal.

Consequently when you get to the leaf where the deletion will be performed, the value can be deleting and leave a valid node.