• tr/// does not do what you think it does. Replace tr with s.
• Add the missing /.
• You have unescaped / characters in your replace string. Either escape them, or change the delimiter.
• $word contains text, not a regexp. Its content needs to be escaped.
• You probably also want to add the g modifier, which indicates you want to replace all occurances (instead of just the first one).

Result:

foreach(loop through each $word in search phrase) {
   $answer =~ s{\Q$word\E}{<b><u>$word</u></b>}g;
}
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Read perlop for details.