ester hydrolysis with NaOH

please see attached

Lose the water molecule from each side ...

why would you do that though

because it is a hydrolysis (using water to break down a compound) so don't you need the water?

Just like in mathematical equations, if something is on both sides of an equation, it just cancels (x + 6 = y + 6 which is just x = y).

Also, when drawing sodium ethanoate it's best not to draw the sodium attached to the oxygen with a covalent bond (-O-Na) - it's ionic

If you use aqueous sodium hydroxide you don't need to use water in the equation. The reagent is the aqueous hydroxide ion. The chemical equation shows only that which reacts and is formed.

RCOOR' + NaOH --> RCOONa + R'OH