You're looking for an element of the  @steps_name array within each element of the  @db_description array. Try something like:

c:\@Work\Perl\monks>perl -wMstrict -le
"my @db_description=(
   'MOVE 3-4 STEPS TO GB FIXTURE', 'WITHIN REACH TO CHECK',
   'GET BEAM', 'PUSH/PULL ( >= 30 CM)', 'BEAM 2-3 TIMES',
   'MOVE 8-10 STEPS TO HOIST',
   );
 ;;
 my @steps_name = ('1-2 Steps', '5-7 Steps', '8-10 Steps', '11-15 Step
+s');
 ;;
 for (my $i = 0;  $i < @steps_name;  $i++) {
   if (grep { /(?i)\Q$steps_name[$i]\E/ } @db_description) {
     print qq{'$steps_name[$i]' FOUND};
     }
   else {
     print qq{'$steps_name[$i]' not found};
     }
   }
"
'1-2 Steps' not found
'5-7 Steps' not found
'8-10 Steps' FOUND
'11-15 Steps' not found
[download]

Update: As a general stylistic note, I would recommend a simpler Perl-style for-loop rather than a C-style loop:

c:\@Work\Perl\monks>perl -wMstrict -le
"my @db_description=(
   'MOVE 3-4 STEPS TO GB FIXTURE', 'WITHIN REACH TO CHECK',
   'GET BEAM', 'PUSH/PULL ( >= 30 CM)', 'BEAM 2-3 TIMES',
   'MOVE 8-10 STEPS TO HOIST',
   );
 ;;
 my @steps_name = ('1-2 Steps', '5-7 Steps', '8-10 Steps', '11-15 Step
+s');
 ;;
 for my $s_name (@steps_name) {
   if (grep { /(?i)\Q$s_name\E/ } @db_description) {
     print qq{'$s_name' FOUND};
     }
   else {
     print qq{'$s_name' not found};
     }
   }
"
'1-2 Steps' not found
'5-7 Steps' not found
'8-10 Steps' FOUND
'11-15 Steps' not found
[download]

Not having to worry about index increments, array accesses, off-by-one errors, etc., is helpful.

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