You need to loop through your list and go through every item, like so:
mycount = 0
for item in List1:
mycount = mycount + item.lower().count('b')
if mycount == 0:
print "It did not work"
else:
print "The letter b appears:", mycount, "times"
Your code doesn't work since you're trying to count 'b' in the list instead of each string.
Or as a list comprehension:
mycount = sum(item.lower().count('b') for item in List1)
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