You could use zsh with its [expression-as-a-glob-qualifier](http://zsh.sourceforge.net/Doc/Release/Expansion.html#Glob-Qualifiers) to select files that only have nine such symbols:

 $ hasnine() { [[ $(grep -c '>' < "$REPLY") -eq 9 ]]; }
 $ mv *.fna(+hasnine) location/

The first line defines a function whose purpose is to create a true/false filter for files that have exactly nine lines with `>` in them. The `grep` command acts on its input, expected in the `REPLY` variable and compares the output to 9.

The second line executes the `mv` command for matching *.fna files to the (example) `location` directory. Matching *.fna files also have to pass the expression qualifier, which is the given as the name of the function we defined.