Under what condition can dividends be declared at the board's discretion?

Dividends can be declared at the board's discretion as long as the corporation is not facing insolvency or is not already insolvent. This means that the board has the flexibility to declare dividends when the financial condition of the corporation allows for it, adhering to state laws and the corporation’s articles of incorporation or bylaws.

The condition described in the correct answer indicates that the board of directors must ensure that the company can meet its liabilities and obligations before declaring a dividend. If the corporation is in a financially stable position and not facing the threat of insolvency, the board is empowered to make decisions regarding dividend distributions for the benefit of shareholders.

In contrast, the other choices introduce conditions that either incorrectly suggest shareholders or meetings dictate dividend declaration or imply that dividends can be declared even when the corporation is in danger of insolvency, which is not permissible under corporate law. This means that boards must operate within the financial limits of the corporation's condition when making decisions about dividends.