A company can buy its own shares when-

Article of Association must authorise and special resolution has been passed for the buy back of shares.

The correct answer is option 4- Article of Association must authorise and special resolution has been passed for the buy back of shares.

When a company acquires its own shares, it is referred to as a 'share repurchase.' Section 68 of The Companies Act, 2013 outlines that a company can repurchase its own shares from the following sources: 
(a) Existing equity shareholders on a proportional basis
(b) The open market
(c) Odd-lot shareholders
(d) Employees of the company

The company can finance the repurchase of its shares using free reserves, securities premium, or the proceeds from the sale of any shares or specified securities. If shares are repurchased using free reserves, the company must transfer an amount equal to the nominal value of the repurchased shares to the 'Capital Redemption Reserve Account.' The following procedures are required for a share repurchase:
(a) The company's Articles of Association must grant authorization for share repurchases.
(b) A special resolution must be passed during the company's Annual General Meeting to approve the share repurchase.
(c) The total amount of shares repurchased in any financial year should not exceed 25% of the combined paid-up capital and free reserves.
(d) The company's debt-equity ratio should not exceed a ratio of 2:1 after the share repurchase.
(e) All repurchased shares must be fully paid-up.
(f) The share repurchase process must be completed within 12 months from the date of passing the special resolution.
(g) The company must submit a solvency declaration to the Registrar and SEBI, signed by at least two directors of the company.