The first thing to do is convert the users input to a DateTime - probably you want to use DateTime.TryParseExact to do that.
You can then use the DateTime.AddMonths method to get the new date, and store that as a DateTime in the database.
Dim [date] As String = "February"
Dim addMonths As String = "4"
Dim dt As DateTime
If DateTime.TryParseExact([date], "MMMM", CultureInfo.InvariantCulture, DateTimeStyles.None, dt) Then
Dim i As Integer
If Integer.TryParse(addMonths, i) Then
dt = dt.AddMonths(i)
"Thanks sir for your solution, if you don't mind can tell me how can save the above record in database"
That bit I can't help you with - there are too many different database systems and table / column combinations for me to give you a simple answer.
However a simple method using a SQL Database would be along the lines of:
Using con As New SqlConnection(strConnect)
Using com As New SqlCommand("INSERT INTO myTable (myColumn1, myColumn2) VALUES (@C1, @C2)", con)
But since I do not know any of your details, you will have to fill them in yourself!