Instead of using the qr// operator to create a regular expression, you quoted it, creating a string "qr/def/m" that you are comparing to $str, which is not found.

Compare:

# Command-line version of OP code 
#   (and added line showing value of $regexp):
$ perl -Mstrict -Mwarnings -le 'my $str = "abc12xdef34xghi56"; 
my $regexp = "qr/def/m"; 
if ( $str =~ $regexp ) { print "MATCHED"; } 
else { print qq"NO MATCH"; } 
print qq"regexp: $regexp";'
NO MATCH
regexp: qr/def/m
[download]

# Command-line version of OP code 
#   (and added line showing value of $regexp), with $regexp corrected:
$ perl -Mstrict -Mwarnings -le 'my $str = "abc12xdef34xghi56"; 
my $regexp = qr/def/m; 
if ( $str =~ $regexp ) { print "MATCHED"; } 
else { print qq"NO MATCH"; } 
print qq"regexp: $regexp";'
MATCHED
regexp: (?^m:def)
[download]

Hope that helps.