Every speller comes face to face at some point with the everlasting conundrum of -ible versus -able. It always appears at first as though there are no rules, no patterns, no guidelines by which to guess what ending the word uses. However, if one parses through enough words, some tendencies become apparent.
The basic rule for this is to drop the suffix and see what remains. If it's a whole word, use -able. If it's not, use -ible. Take, for example "accountable" and "disponible." "Account" is a word. "Dispon" is not. Of course, even the best rules have exceptions, so there are some ways to determine if a word is an exception.
The -ion rule can be incredibly helpful in this pursuit. It's pretty simple. If the base word of the -ible/-able word has a form ending in -ion, it's probably -ible. Think of "combustible." "Combust" is a whole word in itself, but it doesn't use -able because of its noun counterpart: combustion. There's "assertible" too: "assert" is a whole word, but it still uses an i because of "assertion." It's not a perfect rule, but it's a helpful one at least.
However, there's another challenge if the base word ends in -e. There's still the confusion regarding i vs. a, but an additional question is added: should the e stay or go? The e typically only stays if the base word ends in -ce or -ge, assuming they make s and j sounds respectively. In that case, the word would be -eable (but if the -ion rule applies, drop the e and use an i). Otherwise, it will probably be -able. "Pronounceable" and "ageable" are both good examples--"deducible," however, drops the e and uses and i because of the -ion rule.
If all else fails, go by the numbers--four times as many words end in "-able" as end in "-ible."
Of course, none of these rules are constant, and there are plenty of exceptions. Use these rules as a loose guide, though, and you'll start seeing vast improvement in your ability to differentiate between -ible and -able.