conceivable
Able to be imagined or believed as possible.
Conceivable means able to be imagined or believed as possible. If something is conceivable, you can picture it happening in your mind, even if it seems unlikely.
When your teacher says “every conceivable excuse,” she means every excuse anyone could possibly think of. If a scientist says time travel is theoretically conceivable, she means we can imagine how it might work, even though we can't do it yet. When detectives investigate a crime, they consider every conceivable explanation for what happened.
The opposite is inconceivable, meaning impossible to imagine or believe. Before airplanes were invented, flying across the ocean in hours would have seemed inconceivable to most people. What feels inconceivable today might become ordinary tomorrow, which is why scientists and inventors spend so much time thinking about what's conceivable.
When something is conceivable, your mind can conceive of it, or wrap itself around the possibility. You might say “I can't conceive of a reason why she'd do that” when something seems to make no sense at all.