Correct spelling, explanation: there are two similar adjective suffixes often confused: -able and -ible. There are some rules on when to use them, however, there are also many exceptions, and convertible is one of them. Generally, we add the suffix -able to full words (so, if we take the suffix there is a full word left), for example, depend→ dependable. However we also usually add the suffix -ible to Latin-origin words, and convert is one of them. Moreover convertible might have been taken directly from Latin convertibilis, and thus it is spelled like this and not convertable.

Definition of convertible:
adjective, something that can be changed, possible to be converted
This piece of furniture is convertible: it can be a table or a hanger.
noun, a type of car with a folding roof
I’ve always wanted a convertible!

Incorrect spelling, explanation: convertable is a misspelling, as this adjective is written with the suffix -ible, not -able. This may be misleading since usually suffix -able is added to words that remain full without the suffix (for example understand → understandable). Latin-origin words, however, often use the suffix -ible, therefore convertible is the correct spelling.