I imagine the confusion stems from the similar appearance and sound of each of these adjectives combined with a failure to distinguish written English from spoken English. Whatever the cause, the words have related but clearly different meanings. Credible means believable. Creditable means worthy of credit or praise.
Consider the example sentences in the cropped graphic above. The writer has misused the word credible. The correction here requires a replacement.
When speaking of someone’s performance in the context of professional employment, one would not describe that performance as believable. Perhaps if the performance were outrageous or outside the bounds of typical expectations, one might describe the behavior as unbelievable. But believable simply doesn’t work, and so credible (which means believable) doesn’t either.
Extra work may make a report more commendable, and as such a more effective writer could employ creditable to describe that report. In the example shown above, the writer uses credible to describe the report, indicating that management believed the report more because of the statistical analysis it contained. Because this is the message the writer intended to send, credible is an appropriate word in this instance.
Thus, a more effective presentation would replace credible in the first sentence but not the second.