This question can be solved via recursion depth first search. Keep track of the max depth. Traverse left sub tree then traverse right sub tree - increase the depth each level.

Link: Maximum Depth of Binary Tree

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
var maxDepth = function(root) {
    let max = 0;

    let dfs = (node, lvl) => {
        if(!node) return;
        if(lvl>max){
            max = lvl;
        }

        if(node.left){
            dfs(node.left, lvl+1);
        }

        if(node.right){
            dfs(node.right, lvl+1);
        }
    };

    dfs(root, 1);
    return max;
};