破折号后面的两个现在分词短语：proposing the sale of shares in the national oil company, and liberalising the position of women，作“方式状语”，修饰in order后面的不定式。就是说“通过这些方式去实现...现代化”。

His supporters argue that he needed to arrogate more power to himself in order to modernise the country’s society and economy—proposing the sale of shares in the national oil company, and liberalising the position of women. 

【翻译】他的支持者认为，他需要赋予自己更多的权力，以实现国家社会和经济的现代化，——提议出售国家石油公司的股份，解放提升妇女的地位。