He reads the first line
while read file <&6 ;
he reads the 2nd, 3rd and 4th lines
read line1 <&6 read line2 <&6 read line3 <&6
If you want to read the first three lines, consider
$ head -3 rhyme.txt
instead.
Update
If you want to use only read , leave a while and execute:
exec 6< rhyme.txt read line1 <&6 read line2 <&6 read line3 <&6 echo $line1 echo $line2 echo $line3 exec 6<&-
or with a loop:
exec 6< rhyme.txt for f in `seq 3`; do read line <&6 echo $line done exec 6<&-
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