“I want to switch to a new carrier, but I have 6 more months on my contract.”
You have mobile phone service with a certain company, but you are not happy with it. You want to change to a different company, but you can't because you signed a contract with the current company that hasn't finished yet. You are talking about your mobile phone service with a coworker and you say this.
I want to switch to a new carrier, but I have 6 more months on my contract.
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switch to (a service)
To "switch" to a different company or service means to stop using the old one and start using a new one. You can switch to a new company for anything that you use over and over. It wouldn't make sense to say "I switched to a new restaurant, but you could say:
I switched to a new shampoo.
This would mean that you stopped using the shampoo that you always used in the past, and started using a different brand.
a (wireless phone) carrier
The company that you buy wireless phone or wireless internet service from is called your "carrier". This is only used for wireless services. A more general term for a company that you buy a service from is "a provider":
Which internet provider do you use?
have (a length of time) on a contract
To "have" a length of time means that you must continue something for that length of time.
You can use this phrase for things that you are looking forward to the end of, like the remaining time you have in school:
I only have 3 semesters left.
You can also use it for the length of time left for something you enjoy:
We only have 2 more days before we have to go back to work.
"Having" a length of time on a contract means that the contract extends until a certain date, and this is the length of time between now and the end of the contract.
(number) more (days / weeks / minutes / years)
This phrase expresses the number of days, weeks, seconds, months, etc. that are left.
You count starting from now, so "in six more days" means six days from now in the future.