How about:

len(a) - a[-1::-1].index("hello") - 1

Edit (put in function as suggested):

def listRightIndex(alist, value):
    return len(alist) - alist[-1::-1].index(value) -1

If you are actually using just single letters like shown in your example, then str.rindex would work handily. This raises a ValueError if there is no such item, the same error class as list.index would raise. Demo:

>>> li = ["a", "b", "a", "c", "x", "d", "a", "6"]
>>> ''.join(li).rindex('a')
6

For the more general case you could use list.index on the reversed list:

>>> len(li) - 1 - li[::-1].index('a')
6

The slicing here creates a copy of the entire list. That's fine for short lists, but for the case where li is very long, it may be more efficient to use a reverse iteration and avoid the copy:

def list_rindex(li, x):
    for i in reversed(range(len(li))):
        if li[i] == x:
            return i
    raise ValueError("{} is not in list".format(x))

One-liner version:

next(i for i in reversed(range(len(li))) if li[i] == 'a')