string[] formats = {"yyyyMMdd", "MM/dd/yy"};
var Result = DateTime.ParseExact(input, formats, CultureInfo.CurrentCulture, DateTimeStyles.None);
or
DateTime result;
string[] formats = {"yyyyMMdd", "MM/dd/yy"};
DateTime.TryParseExact(input, formats, CultureInfo.CurrentCulture, DateTimeStyles.None, out result);
More info in the MSDN documentation on ParseExact and TryParseExact.
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