I need help writing a complex formula

I'm not a fan of hiding answers in attached spreadsheets, so please allow me to post the approach here, where it can be read without downloading a file. 

=IF(D2="Low",IF(L2="High","Puzzle","Dog"),IF(L2="High","Star","Question Mark")

The first (outer) IF statement checks the value of D2. If it is "Low", then the TRUE part of the outer IF statement will be executed, which contains another IF statement that checks L2. In the same vein, when D2 is not "Low", the IF statement in the False part of the outer IF is executed.  

Written in pseudo-code it looks like this:

if D2 is low then
    if  L2 is high then
         "Puzzle"
    else
        "Dog"
else
    if L2 is high then
          "Star"
    else
         "Plow horse"

Sergei, that is similar to the form I am using. Thank you for finding one with the formulas in it as I had recreated it myself until I got to the Category column.
Monica