Ethos, Pathos, or Logos? If you decide not to come for Thanksgiving, it would break your grandmother's heart. Ethos © Pathos O Logos​

Pathos. The reasoning being, what each word means.
Ethos is essentially the evidence of a “professional,” like things that say “9/10 dentist’s recommend!” By claiming that other people, famous people and/or professionals agree with your statement, it becomes more convincing as a result.
Logos is things such as evidence— the way I remember it is, logos and logic. Statistics are a great example but anything using logic is logos.
Finally, Pathos is emotional. Using someone’s emotions as a convincing factor. Using the commercial example from before, you know those sad puppy dog commercials? “One cent a day can help feed this poor animal.” The entire point is to play with your emotions in order to convince you to pay. That makes it pathos.

So I’m this example this is pathos. You’re trying to make someone feel bad for “breaking your grandma’s heart.” You’re not saying, “your grandma agrees that it would break her heart,” or “your mom and dad both say it would upset grandma,” which would be ethos. You’re also not saying anything logical or statistical. This leaves pathos as your answer.

Hope this helps!