is it right to say through cooling and condensation process if not then how do I say that ?

It's hard to tell without knowing the context.

To synthesise cyclohexanol from cyclohexene, by the addition of cyclohexene to sodium borohydride and boron trifluoride etherate, through cooling and condensation. Followed by the addition of hydrogen peroxide and sodium hydroxide. The product (cyclohexanol) was then purified and used for IR spectroscopy.

No. I wouldn't say that. Do you know what the reaction was? Why was peroxide and lye added. Read this:

https://books.google.com/books?id=3YwOlbZ9FEYC&pg=PA32&lpg=PA32&dq=by+the+addition+of+cyclohexene+to+sodium+borohydride+and+boron+trifluoride+etherate,&source=bl&ots=ED9HuBCsIw&sig=2ZVdVQbJNNQ1carNHtzjdEsA9pE&hl=en&sa=X&ved=0ahUKEwiHz47_oszZAhVBXawKHVGNBZwQ6AEIXTAI#v=onepage&q=by%20the%20addition%20of%20cyclohexene%20to%20sodium%20borohydride%20and%20boron%20trifluoride%20etherate%2C&f=false

what would you say then? I didnt understna what you mean? the paragraph I've sent was the aim of the experiment

Yes, it is correct to say "through the cooling and condensation process."

If you are looking for an alternative way to express the same idea, you can say "by the process of cooling and condensation" or simply "by cooling and condensation." These phrases convey the same meaning and indicate that something is achieved or obtained through the specific process of cooling and condensation.