b get through to (someone) or get (something) through to (someone) : to express something clearly so that it is understood by (someone) I've talked to him many times, but I just can't seem to get through to him. I hope I've finally gotten my message through to him. 6 get through or get through to (someone) : to make a successful telephone call to someone I tried to call home but I couldn't get through. Where were you? I've been trying to get through to you (on the phone) all day! 7 get through or get through (something) : to be accepted or approved by an official group The bill finally got through [=passed] and eventually became a law. The bill finally got through [=passed] Congress and eventually became a law. https://learnersdictionary.com/definition/get

"Get through" can sometimes mean "to succeed in talking to someone on the phone."(definition from Cambridge dictionary) I tried to call her but the signal was bad, so I couldn't get through. "Get through something" has many meanings, though. It can mean that you passed an exam or won a competition. I barely got through my end semester exam, Like you said, it can also mean to finish something. I can get through the work if you help me. In British English, it can mean to use something till it gets finished. We're going through a lot of toilet paper. We need to buy more. I hope this gives you a better understanding.

Soy un gringo. Quizás yo pueda ayudarte a entender este verbo y esta expresión. A menudo lo usamos como una metáfora, pero es mejor entenderlo primero de una manera no metafórica. Un ejemplo: "I am driving into a tunnel. My cell phone will not work. I will call you back after I ***get through*** it. (Estoy conduciendo hacia un túnel. Mi teléfono celular no funcionará. Te llamaré después de que pase por él.) Cuando usamos esta expresión de manera metafórica, generalmente estamos hablando de sobrevivir a algo difícil o terminar una gran cantidad de trabajo. Por ejemplo: "The next few days are going to be a nightmare. I just need to **get through** it, and then we can make some decisions." o "I have so much homework this weekend. It will be a miracle if I can **get through** it all by Monday." Espero que esta explicación sea de ayuda. ¡Buena suerte!

In answer to you question, yes get through can mean to finish something. Scroll 3/4 of the way down the page to get to the phrasal verb, "get through". It's definition #1. https://learnersdictionary.com/definition/get

Get through is a phrasal verb with several meanings. Here are seven of them: get through [phrasal verb] 1 a chiefly US : to finish a job or activity When you get through (with that job), I've got something else for you to do. b get through (something) : to do or finish (something, such as an amount of work) We got through [=covered] all of the material that we wanted to cover. There's still a lot of paperwork to be gotten through. c get through (something) or get (someone) through (something) : to complete or to help (someone) to complete (a test, an exam, etc.) successfully She studied hard and got through [=passed] her exams. The extra hours of study are what got her through her exams. 2 get through or get through (something) or get (something) through (something) : to pass through or beyond something that blocks you or slows you down Traffic was very heavy, but we managed to get through (it). Rescuers are having trouble getting through to the flood victims. : to cause (something) to pass through or beyond something Traffic was very heavy, but we managed to get our truck through (it). Rescuers are having trouble getting supplies through to the flood victims. 3 get through (something) or get (someone) through (something) : to have the experience of living through (something that is difficult, dangerous, etc.) It was a very difficult time in our marriage, but we got through it. I don't know how those early settlers managed to get through [=survive] the winter. : to help (someone) to live through (something) It was pure determination that got them through that crisis. 4 get through (something) chiefly British : to spend or use all of (something) He got through [=went through] all the money he inherited in just a few years. They got through [=went through] three bottles of wine with dinner. 5 a get through or get through to (someone) : to be clearly expressed to and understood by someone I hope my message has finally gotten through to you. [=I hope you finally