This is one of the good reasons for not using
var
all the time ...
Directory.GetFiles returns an array of strings, not FileInformation objects.
And strings don't have a LastWriteTime property.
Try using DirectoryInfo:
DirectoryInfo directoryInfo = new DirectoryInfo(path);
var files = directoryInfo.GetFiles()
.Where(file => allowedExtensions.Any(file.Extension.ToLower().EndsWith))
.OrderBy(file => file.LastWriteTime)
.ToList();