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For completeness, while case has a | OR operator, it doesn't have an AND operator but if using shells with extended glob operators (ksh, zsh, bash), you can implement the AND in the pattern syntax:

• ksh93's @(x&y&z) operator:

    case $string in
      ( @({12}(?)&~(i:[aeiou]*)&*[0123456789]) )
        echo is 12 characters long AND starts with a vowel AND ends in a decimal
    esac
  

• zsh (using ~ (AND-NOT) combined with ^ (NOT)): x~^y~^z

    set -o extendedglob
    case $string in
      ( ?(#c12)~^(#i)[aeiou]*~^*[0-9] )
        echo is 12 characters long AND starts with a vowel AND ends in a decimal
    esac
  

• ksh88, bash, using double negation with OR (!(!(x)|!(y)|!(z)))

    shopt -s extglob # bash only
    case $string in
      ( !(!(????????????)|!([aAeEıiIİoOuU]*)|!(*[0123456789])) )
        echo is 12 characters long AND starts with a vowel AND ends in a decimal
    esac
  

In any case, remember that except in zsh where ranges are always based on codepoint values, ranges like [0-9] cannot be used reliably outside of the POSIX/C locale (hence the [0123456789] instead above).

ksh93 and zsh's case insensitive matching operators (~(i) and (#i)) honour the locale for case sensitive comparison. For instance, in a Turkish locale on a GNU system, (#i)[aeiou] will match on İ, but not I (because uppercase i is İ there). To get a consistent outcome regardless of the locale, you may want to hard code all possible values instead like in the ksh88/bash approach.