这里是不能用“任何”的，要说：我应该怎么办？ 任何的用法：我喜欢吃甜食，任何甜食都可以。

“如何” is a classical Chinese expression, literally it means "as...what". "怎么" is a new expression after "New Culture Movement", literally it means "how (to be/do)". Most of the time, these two words can be exchangeable. They are both correct.

“如何”is classical Chinese usage.It is rarely used in modern spoken Chinese.You could say"我们出去吃饭,怎么样？"“忘了我的学生卡，我应该怎么办？”

Formal: 我们出去吃饭，如何？ Casual: 我们出去吃饭，怎么样？ Formal: (我)忘了我的学生卡，我应该如何是好？(你这么说应该会吸引很多人的注意的。。哈哈。。) Casual.. or normal: (我)忘了我的学生卡，我应该怎么办？

In general, 任何 = any 怎么 = how, why