【小题1】这家公司决定开展一个全国性的广告活动来推广自己的产品。（campaign）
【小题2】在任何情况下我们都不能以牺牲环境为代价来发展经济。(倒装)
【小题3】每个市民都应该尽自己的一份力来抵制在动物身上进行试验。（do one’s part）
【小题4】画廊老板根据自己的经验断言这个年轻人提供的油画是一个赝品。（maintain）The pany has decided to launch a nationwide campaign to promote its products.
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(答案→)The pany has decided to launch a nationwide campaign to promote its products.
解析：
【小题1】The pany has decided to launch a nationwide campaign to promote its products. 其中campaign作名词，活动。
【小题2】Under no circumstances / In no case / By no means / At no time / In no way / By no means should we develop the economy at the cost / expense of the environement. 含有no的短语位于句首时。句子要倒装句。
【小题3】Every citizen should do his part to resist experiments on animals. do his part 意为：尽每个人的一份力做某事。
【小题4】Based on his experience, the owner of the gallery maintained that the painting provided by the young man was (a) fake. maintain 除了“保持”的意思外，还有“断言、宣称”的意思。