"We can conduct electric equipment work and mechanical equipment work in your factories" is grammatically the correct sentence.
1-Work (activity) uncountable noun. ( Cambridge Dictionary)
an activity, such as a job, that a person uses physical or mental
effort to do, usually for money:
I've got so much work to do.
What sort of work are you experienced in?
2-work (CREATION) countable noun something created as a result of effort, especially a painting, book, or piece of music:
The museum has many works by Picasso as well as other modern painters.
The poetic works of Tagore.
3- works (FACTORY) (countable plural)
An industrial building, especially one where a lot of people are employed:
A steel/iron works.
4- works [ plural ] (machine)
the parts of a machine, especially those that move:
If you take the back off this clock, you can see its/the works.
from English Grammar Today
Work as an uncountable noun
Work is an uncountable noun when it means something we do that takes
an effort, often as part of a job or for study:
Hard work is good for you. It keeps you fit. (work as a physical activity)
I’m not going out tonight. I’ve got a lot of work to do. We’ve got
exams next week. (work as study)
We don’t use work with the indefinite article (a) or in the plural.
The word for a specific occupation or task is job, which is a
They offered me a job.
Not: They offered me a work …
We can say that someone is at work when they are at the place where they work and are doing their job:
Can I ring you back later? I’m at work at the moment and I can’t
really talk privately.
Work as a countable noun
Work as a countable noun means something created, especially a book or
painting or piece of music or sculpture:
She bought me the complete works of Shakespeare for my birthday.
Several works of art were stolen from the town museum yesterday.