Comparing array elements using for and if statement

Your issue is that you are iterating over the elements of the array, but then trying to use the element as the index. When you get to the last element of ax, you're trying to do ax[6], which is out of range for the size of ax.

You should do one or the other, ie:

for i in ax:
    if i > 4:
        print('Hi')
   else:
        print('Hello')

or

for i in range(len(ax)):
    if ax[i] > 4:
        print("Hi")
    else:
        print("Hello")

Depending on what your actual goal is here, a more pythonic approach could be a list comprehension:

res = ["Hi" if i > 4 else "Hello" for i in ax]

With this iteration pattern, I would suggest using np.where() as opposed to an explicit for loop:

import numpy as np

ax = np.array([1, 2, 3, 4, 5, 6])
result = np.where(ax > 4, "Hi", "Hello")
print("\n".join(result))

This outputs:

Hello
Hello
Hello
Hello
Hi
Hi

The x Array element is not index so y[x[i]] can out of range.

You can use

for index, value in enumerate(x):
    y[index] # This is correct
    x[value] # This can produce same error :D

Your iteration is wrong, even for a list. To illustrate:

In [321]: alist = ['ab','cd','ef']
In [322]: for i in alist:
     ...:     print(i)
     ...: 
ab
cd
ef

The iteration variable i is an element of the list, NOT an index.

In [323]: i
Out[323]: 'ef'
In [324]: alist[i]
Traceback (most recent call last):
  Input In [324] in <cell line: 1>
    alist[i]
TypeError: list indices must be integers or slices, not str

It does not make any sense to use it as an index. In your case the problem didn't become obvious until you hit the 6, but ax[i] was wrong even before that.

I've seen this mistake in a number of novice questions, and wonder why? Is it just carelessness, or is there some tutorial that's misleading people?

here you go

print(np.where(ax>4, "Hi", "Hello"))

I ran it as below.

x= [1,2,3,4,5,6]
y= [5,6,7,8,9,10]

ax=np.array(x)
ay=np.array(y)

for i in ax:
    if i>4:
        print("Hi")
    else:
        print("Hello")