Yes, if you have a Part-Time and a Full-Time job, you should give each employer a W4.
On Form W-4, section 2, you can select that you have more than one job. There is a Worksheet on page 3 and a table on page 4 to help you figure out how much extra you need to have withheld. You can choose to leave your PT job not withhold taxes and have the extra withheld from your FT pay or you can have your PT employer withhold taxes on that income by entering the additional amount you want withheld in Step 4c
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