I have a script which is using the EXIF data from a JPG file to find the DateTaken value. Once found, place the data in $Year and $Month
The date-and-time string returned by $objFolder.GetDetailsOf($File, 12) contains invisible control characters[1], for reasons unknown to me.
You can strip them as follows, after which your code should work:
# Remove the formatting control characters from the string, by replacing
# all instances of Unicode character category \p{Cf} with the empty string.
# For more info on Unicode categories, see http://www.regular-expressions.info/unicode.html
$dateTimeStr = $objFolder.GetDetailsOf($File, 12) -replace '\p{Cf}'
[int] $yeartaken = $dateTimeStr.Split("/")[2].Split(" ")[0]
[int] $month = $dateTimeStr.Split("/")[1]
$monthname = (Get-Culture).DateTimeFormat.GetMonthName($month)
As an aside, on a general note: Ansgar Wiecher's answer shows more robust date-time string parsing techniques.
[1] In my test file's metadata I found instances of Unicode control characters U+200E (LEFT-TO-RIGHT MARK) and U+200F (RIGHT-TO-LEFT MARK)