What’s the difference between “書けるか“ and “書けますか” (Can you write?). I read the rule for the potential form, but then in an example it said ます on the end instead of る. So do both work and what’s the difference?
Both 書ける and 書けます (and so too 書けるか and 書けますか) have the same meaning, in so far as both are a non-past potential form of the same verb, 書く. However, 書ける is the 'plain form' of the potential verb, while 書けます is the 'polite form' (or 'ます form') of the non-past potential verb.
The difference between them is that you are conveying a sense of politeness towards the listener in using the ます-form of the verb. You might use this with a stranger, or someone who is senior to you in some way (e.g. age, job position).
Conversely, you would ordinarily only use 書ける with someone who you are friends with, or someone who is junior to you in in some way.
As a rule of thumb, it's best to stick to ます-form over plain form if you are in doubt as to your relationship with the listener; but, as posts such as How do Japanese speakers transition from polite to plain form amongst friends? or Can polite and casual Japanese be combined? show, the decision as to whether/when you use the ます-form versus plain form of a verb can be somewhat more nuanced.