Question might be wrong. If you pop the node off then add 3 children, your queue should have 3 children, presuming there’s no siblings in the queue. From the answer, you want to know what the length of the queue will be, not how much in will increase by. If I’m understanding correctly, you want to ask something like “If the root node to be searched has 2 children and is not the value being searched for, the length of the queue will be 3 at the end of the search loop.”

Edit: if you’re looking for the total difference in queue size for the loop, saying ‘at the end of the loop’ is misleading since you decrease the size at the beginning of the loop, then add children at the end of the loop.

True or False: If the next node to be searched has 3 children, the length of the queue will increase by 3 at the end of the search loop.

True:

Not quite. Since the searched node has to be popped off the queue, the length of the queue will first decrease by 1, then increase by the number of the searched node’s children for a total length of 2.