A family of Microsoft relational database management systems designed for ease of use.
You can do it with code:
Dim strSQL As String
strSQL = "INSERT INTO tblVaccine(Account_Number, DateAdm, VaccineName) " & _
"VALUES(" & Me.Account_Number & ",#" & Format(Me.DateAdm ,"yyyy-,mm-dd") & "#,""" & _
Me.HepBvaccine & """)"
CurrentDb.Execute strSQL, dbFailOnEror
This assumes that Account_Number is a number data type, DateAdm a date/time data type, and VaccineName a text data type.
You say the table is unrelated, but reading between the lines, it looks to me as though tblVaccine is referencing whatever table the form is bound to in a many-to-one relationship type on Account_Number and DateAdm, which I take to be a composite candidate key of the referenced table, in which case you could do this without any code by means of a subform bound to tblVaccine and linked to the parent form on Account_Number;DateAdm. All you'd then need would be a combo box in the subform bound to the VaccineName column from which to select the vaccine.