You can convert the input/output strings to conversion numbers by using an enum. This has the advantage of greatly simplifying your code, as well. You must, however, make sure the strings in your list exactly match the names in your enum. This simple algorithm will convert from any input to any output.
enum Conversions
{
Inches = 1,
Feet = 12,
Yards = 36
}
private void convertButton_Click(object sender, EventArgs e)
{
int fromDistance = 0;
int toDistance = 0;
fromDistance = int.Parse(distanceInput.Text);
Conversions measureinput = ((Conversions)Enum.Parse(typeof(Conversions), fromList.Items[fromList.SelectedIndex].ToString());
Conversions measureoutput = (Conversions)Enum.Parse(typeof(Conversions), toList.Items[toList.SelectedIndex].ToString());
toDistance = (fromdistance * (int)measureinput) / (int)measureoutput;
distanceOutput.Text = toDistance.ToString()+ " " + Enum.GetName(typeof(Conversions), measureoutput);
}