How Do I Add Even Numbers Between Two Numbers Together?

There's no need for a loop to do this:

public static int SumOfEvenNumbersBetween(int start, int end)
{
    if (end < start) 
    {
        // Swap the arguments if necessary:
        return SumOfEvenNumbersBetween(end, start);
    }
    
    if (start < 0)
    {
        // Handle negative ranges:
        if (end < 0) return -SumOfEvenNumbersBetween(-end, -start);
        return SumOfEvenNumbersBetween(0, end) - SumOfEvenNumbersBetween(0, -start);
    }
    
    // The number of evens between 1 and the start of the range (exclusive).
    int m = (start - 1) / 2;
    
    // The number of evens between 1 and the end of the range (inclusive).
    int n = end / 2;
    
    // The sum of the first n even numbers,
    // minus the sum of the first m even numbers:
    return (n * (n + 1)) - (m * (m + 1));
}

Public Shared Function SumOfEvenNumbersBetween(ByVal startNumber As Integer, ByVal endNumber As Integer) As Integer
    If endNumber < startNumber Then
        ' Swap the arguments if necessary:
        Return SumOfEvenNumbersBetween(endNumber, startNumber)
    End If
    
    If startNumber < 0 Then
        ' Handle negative ranges:
        If endNumber < 0 Then
            Return -SumOfEvenNumbersBetween(-endNumber, -startNumber)
        End If
        
        Return SumOfEvenNumbersBetween(0, endNumber) - SumOfEvenNumbersBetween(0, -startNumber)
    End If
    
    ' The number of evens between 1 and the start of the range (exclusive).
    Dim m As Integer = (startNumber - 1) \ 2
    
    ' The number of evens between 1 and the end of the range (inclusive).
    Dim n As Integer = endNumber \ 2
    
    ' The sum of the first n even numbers,
    ' minus the sum of the first m even numbers:
    Return (n * (n + 1)) - (m * (m + 1))
End Function

The sum of the first n positive even numbers is n × (n + 1).

For positive ranges, you just need to calculate the sum of the first n even numbers, and then subtract the sum of the first m even numbers, where m is the number of even numbers before the start of your range.

For purely negative ranges, you just need to swap and negate the arguments, and then negate the answer. For example, the sum of the even numbers between -9 and -1 is the negative of the sum of the even numbers between 1 and 9.

For ranges which straddle zero, break them into two parts, apply the previous rules, and then combine the results.

The code looks slightly more complicated than the loop / LINQ answers in your reposted version of this question[^], but for large ranges, it will be much faster.

EDIT: Added VB.NET version of the code to match the tags.