red-handed
Caught in the act of doing something wrong, with proof.
Red-handed means caught in the act of doing something wrong, with clear proof of guilt right there in the moment.
When a teacher catches a student red-handed copying answers during a test, there's no room for excuses or denials. The evidence is right there. If your parents walk into the kitchen and find you red-handed with cookie crumbs on your face and the cookie jar in your hands, you can't pretend you were just admiring the jar's design.
The phrase always involves being discovered during or immediately after the act, not hours or days later. Being caught red-handed is different from being suspected or accused: it means the proof is undeniable and obvious. A security camera might catch a thief red-handed, or a referee might catch a player red-handed committing a foul.
People sometimes use it playfully too. You might catch your little brother red-handed sneaking your Halloween candy, or catch your dog red-handed digging in the garden with muddy paws.
Note: Red-handed is usually used as an adjective (“caught red-handed”), not an adverb.