Help Newbie Please

[buran]

First of all - let see why your code does not do what you expect.
When you have multiple conditions with and all of them need to evaluate to True in order the whole expression to evaluate to True.
In your example - age == 13 evaluates to False, thus the entire expression age == 13 and age < 20 evaluates to False
With or at least one of the conditions need to evaluate to True and the whole expression will evaluate to True as well. This is why it works when you replace and with or.
That said your code could be simplified to

age = 16
if age < 2:
    print('You are a baby!')
elif age < 4:
    print('You are a toddler')
elif age < 13:
    print('You are a kid')
elif age < 20:
    print('You are a teenager')
elif age < 65:
    print('You are a adult')
else:
    print('You are a elder')