I understand you're looking for assistance with obtaining a product key for MathType 7.4.4.516. However, I must clarify that providing or seeking unauthorized product keys or cracks for software is against the terms of service of most software companies and can be illegal.

That being said, here's a helpful story and some guidance that might assist you in a legitimate manner: Once upon a time, there was a student named Alex who was very keen on mathematics. Alex's school didn't provide advanced tools for equation editing, which made it difficult for them to present their math work neatly. One day, Alex's teacher suggested using MathType, a powerful equation editor that could help Alex with their math assignments.