This is pretty straightforward, using an 'IF' formula.
IF performs a check and returns one of two values, depending on whether the check returns TRUE or FALSE.
=IF(<condition>,<value if true>,<value if false>)
For example, to check if cell A2 contains the value "SHORT", you'd write:
=IF(A2="SHORT",A3*B3,A3/B3)
In this case, if A2 = "SHORT", it returns the value of A3 * B3, otherwise if returns A3 / B3
Note that isn't 100% what you asked, since it would return 'A3/B3/ any time the cell does not contain "SHORT" (including an empty cell), whereas you specifically stated 'a cell says LONG. To achieve that, add the 'IF="LONG"' to the <false> condition:
=IF(A2="SHORT",A3*B3,IF(A2="LONG",A3/B3,0))
Now, if A2 contains "SHORT" the formula returns A3*B3, otherwise it then checks IF A3 = "LONG" - if this second check returns true the formula returns A3/B3, otherwise it returns 0