I had a person in my party a level 4 wizard memorize a level 4 spell. she memorized it and its in her spell book but there is no box on the left to put it in. any ideas?

Wait... your level 4 mage cannot have level 4 spells. A level 4 mage only gets 3 level 1 and 2 level 2 spells, unless specialised, in which case they get one extra in each level. To get level 4 spells your mage must be level 7 at least.

Edit: For further clarification, your mage can 'learn' higher level spells, ie. put them in her spellbook, but they may not be used until she reaches the required level. That is why you don't see an available memorisation slot.

No, it doesn't change a thing. Look at my previous reply again: a level 4 mage only gets level 1 and level 2 spells. She will not get level 3 spells until she is caster level 5. Here is a shorthand of what level spells your mage can use at each caster level:

Mage level 1 -- Level 1 spells
Mage level 2 -- Level 1 spells
Mage level 3 -- Level 1 and 2 spells
Mage level 4 -- Level 1 and 2 spells
Mage level 5 -- Level 1, 2 and 3 spells
Mage level 6 -- Level 1, 2 and 3 spells
Mage level 7 -- Level 1, 2, 3 and 4 spells
Mage level 8 -- Level 1, 2, 3 and 4 spells
Mage level 9 -- Level 1, 2, 3, 4 and 5 spells

I'm assuming you're playing BG1, so I won't go any higher.

that's very helpful. thank you. yes im playing BG1

in the game's manual there are a lot of tables with info on character progression. If you haven't installed any mod or something that alters that, you should look there.