lots of extra brackets there!, also, an "else" cannot have a conditional, so you need another "elsif", use "else" for a catchall at the end, ive fixed up your snippet below:

if ($name =~ /^derrick\b/i) 
{
    print $phnums{"derrick"};
} 
elsif ($name =~ /^juan\b/i) 
{
    print $phnums{"juan"};
} 
elsif ($name =~ /^kevin\b/i) 
{ 
    print $phnums{"kevin"};
}
else
{
    print "No such person!\n";
};
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