My step-son is 18 and will graduate high school on 6/18. We have him full time.
My husband's ex pays $1,204 per month (payable half on the 1st and half on the 15th via wage garnishment.)

It is my position that she has to pay the entire month's worth ($1204) because his graduation is after 15th. She is saying that because he graduates on 6/18, she only has to pay 18 days of the month.

Who's right?

Tell her to give him the difference as a graduation present.

What does the child support agreement state? If support is paid by garnishment, then what does the agency that issued the garnishment say. Her job will have to continue deductions until they receive an order from the agency or the court to stop it.

His ex is correct (I'm assuming you are in California because you sound like it).

Child support ends as a matter of law (meaning you do NOT have to modify the support order, although a modification of the wage assignment is necessary to stop it) when the child graduates from high school if he is 18. So, if the graduation is mid-month, support would be prorated up to the date of graduation. If the wage assignment pays the second half of a full month's support on the 15th, your husband will owe a prorated portion back to his ex (the portion covering 6/18 - 6/30).

Sorry, that's just the way it works.

If the child goes to college full time does hs dad have to pay for his support? He turned 18 today and the garnishment ended.

If the child goes to college full time does hs dad have to pay for his support? He turned 18 today and the garnishment ended.

If your support order is from California, no. There is no such thing as college-level support in California. That simply does not exist.