Answer based on context:

With Upper Burma securely under his control, Nyaungyan's successor Anaukpetlun marched south. His 14,000-strong land and naval forces sacked Prome on 13 July 1608 after a bloody siege of eight months. His 12,000-strong forces then attacked Toungoo, then ruled by his cousin, Natshinnaung, in August 1610. After a siege of 23 days, Natshinnaung agreed to become a vassal on 4 September 1610. But Natshinnaung was deeply unhappy with his reduced status, and secretly invited de Brito of Syriam to attack Toungoo. In July 1612, Syriam and Martaban forces ransacked the city for ten days, and left, taking Natshinnaung to Syriam. In response, Anaukpetlun's army of 13,000  left Ava for Syriam on 26 December 1612. A flotilla of 80 war boats and 30 cargo boats  was also sent down the Irrawaddy to blockade the port. The Burmese forces overcame Portuguese outer defences, and finally blockaded the port on 24 February 1613. But Portuguese gunners and musketeers kept the Burmese at bay for 34 days while waiting for reinforcements from Goa to arrive. On 29 March 1613, however, the Burmese successfully brought down a section of the walls, from their tunnels below. The city was sacked. On 7 April 1613, de Brito his son and Natshinnaung were all executed by impalement. A month later, on 14 May 1613, Binnya Dala of Martaban, submitted. The ruler was nominally tributary to Siam but had ruled the region like a sovereign since the death of Naresuan in 1605. Alarmed, the Siamese sent an army to Ye, south of Martaban, to prevent the Burmese from marching down the coast. But the Siamese did not try to retake Martaban.

When did the seige of Prome begin?
1609-November-13