2014 Hyundai Elantra GT - What is this thing?

what is a intake vvt solenoid

Hyundai Elantra GT Variable Valve Timing (VVT) Solenoid Replacement Costs (yourmechanic.com)

Symptoms of a Bad or Failing Variable Valve Timing (VVT) Solenoid | YourMechanic Advice In your case, the solenoid for the intake valve (duh!) would be the problem.