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No. You only owe California tax on days you were physically present and working in California. Your employer should list Utah wages and withholding (and possibly six days of CA income).

It’s doubtful your employer would break out any CA income for a business trip. They would leave it to you to report that on your own.

As Tax Expert @MonikaK1 said, file a nonresident California income tax return (because you did work for 6 days in CA). Utah will give you credit for any tax paid to CA.

On “Did you earn all your income in California” say NO and enter your California earnings.