I am a single mom with 2 kids and work #1 job that pays 23,000 per year and I have just picked up a #2 job that will pay 21,000 per year. I don't want to owe taxes at the end of the year. What should I claim on my w-4 for the 2nd job?
The W-4 should have a worksheet for multiple jobs, so you could start with that. Then after you get a paycheck, see how much tax will be taken out for the year and compare it to an estimate of your tax liability for the year.
According to this basic tax estimator, with a $46,000 income and 3 exemptions, your annual tax liability would be about $2,600. (this assumes no other income and no itemized deductions for mortgage interest, charities, medical expenses, etc.) If you don't want to be surprised with a tax bill at the end of the year you could be conservative and withhold enough to cover that with some extra cushion.
The general rule of thumb on a second job is to take zero exemptions. So if you follow the worksheet, it might tell you to mark in 4 or 3. However, you already marked those on your first job. So put in 0 for the second job.
You can double check this with the tax estimator posted in the other answer. $44,000 income, 3 exemptions, 2 dependent children as head of household gave $720 as your total liability. Putting in $23,000 income with the 3 exemptions and 2 dependent children gave zero liability for the first job. Putting in $21,000 with zero exemptions gives $1170 from the second job. So if their withholding matches that, you'd get a refund of around $450.
Another way of looking at it is that you need to withhold about $14 a week. If you're withholding more than that between the two jobs, you could cut back. If you're withholding less, then you should add more if you don't want to owe anything.
I think that you have extra exemptions after your first job. So two exemptions on your second job will probably produce the correct result. Then you wouldn't get much of a refund. However, as I said, you should verify this on your actual paychecks.
The safest way is to do the zero exemptions on the second job's W-4. Worst case, you overwithold and get a refund. You'll lose out on a bit of interest income, but interest rates suck anyway. Losing $5 for peace of mind may be worth it.