How do I claim childcare expenses for my two grandsons who resided with me for only 4 months?

[xmasbaby0]

Sorry---you don't.    You cannot claim children who you only had for four months as dependents so you cannot claim the childcare credit for them.    You did not have them long enough to claim any child-related credits.

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent

https://ttlc.intuit.com/questions/3113432-who-can-i-claim-as-my-dependent

[Opus 17]

There may be a way that you could claim your grandchildren as dependents, which I will discuss in a moment, but even if they qualify to be your dependents, you they don’t qualify for the child care expense credit, to be a qualifying person for the child and dependent care credit, the child must live in your home more Than half the year.  

If the children lived more than half the year in the home of another relative, such as a parent, grandparent, uncle, or aunt, then only that person can claim them as dependents and you cannot.  If the children moved around and did not spend more than half the year in any single home, then you could claim them as dependents but only if you get a signed multiple support agreement from everyone else who provided a home for the children, that indicates that they are allowing you to claim the children as dependents.