A right-handed screw (the normal kind) must be turned clockwise into the wood (viewed from its head).

The cross product of two vectors is perpendicular to both; the right hand rule picks the one out of two possible perpendicular directions.

The diagrams show the right hand rule.
The order of operands is **important**.
The result of
**u** **×** **v**
points in the same
direction a screw must
point if
twisting from **u** to **v**
drives it into the wood.

Or, think of the direction your
thumb points when your fingers curl
around from **u** to **v**.

Does
**u** **×** **v**
point in the same direction as
**v** **×** **u** ?
(Hint: get out your screw driver).