"Slam" is generally used with doors, objects, or as "slam into" (collide). It is not idiomatically correct to say "slam a person's face."
Step 1: Examine each usage.
(a) "The door slam" - correct verb usage.
(b) "Slammed down the phone" - idiomatic and correct.
(c) "Slammed his face" - inappropriate, as "slam" is not normally used with a direct human object like "face." The common usage is "slap" or "hit."
(d) "Slammed into a tree" - correct phrasal usage meaning "crash violently."
Step 2: Conclusion.
Option (c) is the incorrect/inappropriate usage. \[ \Rightarrow \boxed{(c)} \]
"Slam" typically collocates with objects that can be forced shut, thrown down, or crashed into with a loud, sudden impact, such as doors, phones, and vehicles. Check whether each object fits that pattern.
Only "slammed his face hard" uses "slam" with an object it doesn't normally take.
Hence, the correct answer is She slammed his face hard.