According to the Insolvency Act 1986, which of the following is/are possible grounds for a compulsory winding up?

A company can indeed be wound up by the court if it has passed a special resolution to this effect. This is a clear ground for compulsory winding up as specified in the Insolvency Act 1986. A special resolution indicates the company's decision to cease operations, and when a company expresses such intent, the court can enforce this by initiating the winding-up process.

In the context of other options, a public company failing to obtain a trading certificate within one year of incorporation represents a situation where the company is not legally allowed to trade, which can be a cause for winding up under certain circumstances, but it's not universally recognized as a straightforward ground for compulsory winding up. Similarly, a company failing to commence business within six months may raise issues regarding its viability and could be a relevant factor for winding up, but again, it's not the most direct ground listed in the act itself. These conditions could lead to winding up in specific cases, but they do not have the strong direct authority that a special resolution provides for the court’s action.