Alternate or alternative?
In most cases, these two words have very different meanings.
Alternate basically means ‘this way, then that way’, or ‘by turns’. If you’re a member of the plant genus Hebe, your leaves grow in alternate [adj.] pairs on each stem. Two leaves point this way, the next pair that way, the next pair this way, and so on.
Or, you can arrange with another member of staff to work from home on alternate Wednesdays: she does this week, you do next week, and so on.
You can alternate [v.] between two points of view: ‘Should I buy the pink, or the blue? The pink. No, wait – I prefer the blue. No . . . curses . . .’ Similarly, the alternator in a car is a gizmo that handles alternating currents (the current flows this way, then the opposite way, then this way again, etc.).
Alternative essentially means ‘other’, or, very similarly, an option on choices. So, if you have no alternative but to comply, you have no other option. If you hold an alternative point of view, then it is essentially another point of view.
But . . .
There is, unfortunately for my pedantic nature, a degree of blur in North America, where ‘alternate’ [adj.] is an acceptable alternative to ‘alternative’. You can, for instance, take ‘the alternate route home’, to quote the Merriam Webster dictionary.
Still, by now, at least, if you know what you want to say, and if you know where you live, you can make an informed choice.