If it is exactly that line in every file, and not just "the first value larger than 8" y You could just play games with the input record separator.
UPDATE: Sorry, misread question. Changed program. Note that your data set has a line that ends in "SIL" before the one you highlighted in red. If you want everything up to the SECOND line ending in "SIL" just repeat the "print" line.
{
local $/ = "SIL\n";
#open my $in, '<', $whatever or die "$!";
#open my $out, '>', $output or die "$!";
#print $out scalar <$in>;
print scalar <DATA> for 1..2;
}
__DATA__
0.642375 125 SIL
1.0705 125 ઔર્
1.3651875 125 આત્
1.519875 125 મ
...
...
...
7.2140627 125 સે
7.478125 125 હટ્
7.622625 125 જા
7.956125 125 ઓ
8.192375 125 SIL
8.252 125 SIL
8.464 125 SIL
8.706 125 SIL
