To find the inequality that represents Genevieve's situation, we start by determining how much money she needs to save. She currently has $56 and wants to have at least $200.
- The total amount of money she wants is $200.
- She currently has $56, so the amount she needs to earn is \( 200 - 56 \), which equals $144.
- If she works \( x \) hours at a rate of $12 per hour, she will earn \( 12x \) dollars.
Now we can set up the inequality: \[ 12x + 56 \geq 200 \] This states that the money she earns from her work plus what she has saved should be greater than or equal to $200.
Thus, the correct inequality is: \[ \boxed{12x + 56 \geq 200} \]