請參考《資料結構》教材解決這個問題。

class BiTree {
	private int data;
	private BiTree left;
	private BiTree right;

	public BiTree(int x) {
		data = x;
	}
	
	//小的數放左邊，大的數放右邊
	public void add(BiTree t) {
		if (t.data < this.data) {
			if (left == null) {
				left = t;
			} else {
				left.add(t);
			}
		} else {
			if (right == null) {
				right = t;
			} else {
				right.add(t);
			}
		}
	}
	//中序遍歷，先左子樹，再自身，再右子樹
	//遞迴思想
	public void travel() {
		if (left != null) {
			left.travel();
		}
		System.out.print(data+" ");
		if (right != null) {
			right.travel();
		}
	}
	
	//求高度
	//遞迴思想
	public int height(){
		int treeHeight = 0;
		int leftHeight,rightHeight;
		if(this == null){
			return 0;
		}else{
			leftHeight = (left == null? 0:left.height());
			rightHeight = (right == null? 0:right.height());
			treeHeight = Math.max(leftHeight, rightHeight);
			return 1+treeHeight;
		}
	}
}

public class My1 {
	public static void main(String[] args) {
		BiTree t = new BiTree(12);
		t.add(new BiTree(9));
		t.add(new BiTree(5));
		t.add(new BiTree(8));
		t.add(new BiTree(15));
		t.add(new BiTree(20));
		t.add(new BiTree(11));

		t.travel();//遍歷
		
		System.out.println();
		System.out.println("樹的高度是："+t.height());
	}
}
 

Conclusion
5 8 9 11 12 15 20 
樹的高度是：4