This double negative pattern softens a statement. It means 'it's not that ~ is not the case,' so it implies that something is possible or true, but with hesitation or understatement. For example, if you say 行けないことはない, you mean 'it's not that I can't go'—so you can go, but maybe with difficulty or reluctance. It often carries a nuance of 'if I try' or 'under certain conditions.' Use it when you want to avoid a direct positive assertion, like admitting ability but not enthusiasm, or acknowledging a fact while hinting at exceptions. It is a conversational pattern, though not overly casual, and can be used in both spoken and written Japanese. Note that the verb must be in the negative form, and the structure is a bit like 'there is no (situation) where it is not ~.' This pattern is not as strong as saying 'I can do it' outright; it leaves room for doubt or condition.