Can I file head of household, my daughter and her three children, moved in with me in April of 2022, I pay for all of the rent, electric, heat and water?

[xmasbaby0]

Maybe.   But did your daughter have any income?   Provide some details.  We do not know enough to determine whether you can claim any of them as dependents, and in order to file as Head of Household you have to have a qualified dependent.

Am I Head of Household?

https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household

https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household

If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.

[Hal_Al]

In order to claim Head of Household (HoH), you must be claiming at least one of them as a dependent. Even if your daughter doesn't qualify as your dependent, her children (almost certainly) do. Essentially, it's optional whether you or your daughter claim all or some of her children (subject to rule 6 below). You can split them any way she wants and allows. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

A child closely related (grandchild counts)to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled
2. He did not provide more than 1/2 his own support
3. He lived with the relative (including temporary absences) for more than half the year
4. He is younger than the relative (not applicable for a disabled child)
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
6. If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child (you must have a higher income than your daughter). 

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...