Isn’t this the Midterm question?
First of all, we show this calculation (but with slightly different numbers for the resistances) in the last video of Unit 3. That may answer your question.
Your first step above is correct – to calculate the circuit current using the total resistance.
However, look at the next step, where you calculated P using current and resistance. We asked for the heat generated by the loose connection only.
(Your next guess, using P = VxI will only work if you calculate and then use the voltage drop across the loose connection, not the source voltage.)