Translation:Please write using a pen.
This is what is causing some confusion to me. Both verbs are in the TE form, which means that both could be orders right? Is there a rule that the first verb modifies the second? Wasn't there a rule the TE form verbs assume the conjugation of the last verb in the phrase? I'm still confused...
ください essentially means 'please'. Earlier in the course, you came across sentences like みずをください (give me water please). In that case, the 'give me' is implied, just as if you said 'water please' in English.
With this sentence, there are two ways that you can tell that it is a request. First, notice that the verb 書いて is in the て-form. One common use of the て-form is for commands. やめて - Stop! Add ください (please) to your て and that command becomes a request. やめてください - Please stop.
So here we have: ペンをつかって Using a pen 書いてください please write.
I've read the other comments and I think I understand the subtle meaning differences, but I would have gravitated more naturally to "ペンで書いてください” where all the individual parts are marked by particles; but in this example I'm noticing a distinct lack of any kind of particle between "つかって” and "書いて”. Is "つかって書いて” treated as a "single command" of sorts? Or is there some kind of colloquial abbreviation happening?