Good question! It is very important to understand this both for logic games and logical reasoning.
"All Labrador retrievers bark a great deal." If it's a Labrador, it's going to bark a great deal. No exceptions. L - - - - - - - - - - -> BGD
From this, we can create a contrapositive. If it doesn't bark a great deal, then it is not a labrador. not BGD - - - - - - - - - > not L This is why A is the correct answer.
Let's look at D. Can we say, "If it's not a Labrador, then it doesn't bark a great deal?" No. This is not a valid conclusion. What about Bernese Mountain Dogs? Yorkipoos? Rat Terriers? These dogs could all bark a great deal. If the passage said, "only Labrador Retrievers bark a great deal," then D would be correct. However, we only have enough information to make a conclusion about Labradors, so we cannot conclude D.