Do you infer what I'm implying?

Infer this.

In an episode of Law & Order SVU, two cops have an exchange with a suspect:

Cop: What'd he do aside from keeping the victim from the cameras, thereby saving your five-star ass?
Suspect: He gave us no choice. He hasn't shown up for work since the event.
Cop: How convenient. The only employee that can testify in court.
Suspect: What you're inferring is preposterous.
Cop: Implying.
Other cop: You did infer what he implied.
Cop: But on the bright side, you did infer correctly.

By now the suspect should be ready to confess.

Here's the rule on these two words: Imply and infer are opposites, like a throw and a catch. To imply is to hint at something, but to infer is to make an educated guess. The speaker does the implying, and the listener does the inferring.

You'll just have to memorize them.

Imply comes from the Latin implicāre, meaning to implicate. Infer comes from the Latin inferre, which means to bring into.

So you can study Latin, or, as I suggested, just memorize them.

Some unruly types imply that infer can be used to mean imply, but don't infer anything: when we catch them, they're going to the slammer. Don't even think about it.