1. I think the promotion is actually going very well.
我認為促銷進展得真的很不錯。
還能這樣說：
I think our promotion is very good.
I'm satisfied with our promotion.
諺語：
Think well before you act.
請三思而后行。

2. I wish us to succeed in our business transaction.
希望我們生意興隆。
還能這樣說：
I hope our transaction goes well.
Wish us a good luck in business.
應用解析：
hole-and-conner transactions 秘密的交易，偷偷摸摸的交易

3. We have made a very good start in our business.
我們在業務上有了良好的開端。
還能這樣說：
Our business has a good beginning.
Our business has started successfully.
諺語：
Clumsy birds have to start flying early.
笨鳥先飛。

4. We hope for long term cooperative relationships with customers through our high quality products and competitive prices.
我們真誠希望憑借自己高質量的產品和有競爭力的價格與客戶建立長久的業務聯系。
還能這樣說：
We hope we can maintain a close partnership with our customers by keeping high quality products and competitive prices.
We hope that the high quality products and competitive prices can bring us long term cooperation with the customers.
應用解析：
commercial partnership 商業合伙；
family partnership 家庭合伙；
joint-venture partnership 聯營，合營