Student or Learner
I am not sure how to write this sentence:
I know that companies and boards cut all the costs in budget in down economy periods, till new good scenarios.
OR have to write
I know that in down economy periods, companies and boards cut all the costs in budget till new good scenarios.
Which is the correct one or better one?
During times of economic decline, I know that companies and boards cut costs across the budget until conditions improve.
I don't think "down economy periods" is the correct term. I've heard of "economic downturn" or "periods of low economic growth" or "periods of economic decline". I'm not an economist myself, so I'm not sure exactly what term would be most appropriate. Likewise "new good scenarios" does not seem like a commonly used phrase for discussing improving market conditions. You would also need a verb to go with the noun phrase.
To "cut all the costs in the budget" could also be expressed "cut all budget costs". However, this could be confusing, since it might mean that they cut the entire budget.
Once you've cleaned up the parts, both of the arrangements you have could work.