Firstly: 

We ask Allah, may He be exalted, to have mercy on your father and forgive him, and to have mercy on all the deceased Muslims, for He is All-Hearing, All-Responsive. 

Secondly: 

If a woman’s husband dies, if she is pregnant her ‘iddah ends when she gives birth, because Allah, may He be exalted, says (interpretation of the meaning): “And for those who are pregnant (whether they are divorced or their husbands are dead), their Iddah (prescribed period) is until they deliver (their burdens)” [at-Talaaq 65:4]. 

If she is not pregnant, then her ‘iddah is four months and ten days, because Allah, may He be exalted, says (interpretation of the meaning): “And those of you who die and leave wives behind them, they (the wives) shall wait (as regards their marriage) for four months and ten days” [al-Baqarah 2:234].

 Thirdly: 

The woman whose husband has died must observe ‘iddah following the lunar calendar, not the solar calendar, because the Islamic rulings are based on lunar months. 

Months are to be counted by new moons if the husband died at the beginning of the month. If some months are thirty days and others are twenty-nine days, then the counting is still correct and the woman in ‘iddah does not have to make up any of the days from the months that were twenty-nine days. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (29/315-316): Counting the months of the ‘iddah in the event of divorce, annulment or death of the husband, is to be based on the lunar, not solar, calendar. If the divorce or death occurred at the beginning of the month, then the months are to be counted by the new moons, because Allah, may He be exalted, says: “They ask you (O Muhammad SAW) about the new moons. Say: These are signs to mark fixed periods of time for mankind and for the pilgrimage” [al-Baqarah 2:189], even if that falls short by a few days, because Allah has commanded us to observe ‘iddah by the months. He, may He be glorified, says: “their Iddah (prescribed period) is three months” [at-Talaaq 65:4] and  “four months and ten days” [al-Baqarah 2:234]. So attention must be paid to the months, whether they are thirty days or less. End quote. 

But if he died during the month – as in the case mentioned in the question – then she should observe ‘iddah for the remainder of the first months and for three months thereafter, with their new moons, whether they are twenty-nine or thirty days, plus ten days, then she should add whatever she missed of the first month. There are two ways to work out what she missed of the first month 

1.     She may regard the first month as thirty days, whether the month in which the event occurred was thirty or twenty-nine days, and if she observed ‘iddah for twenty days of that month, she should complete ten more days in the fifth month, and so on.

2.     She may observe ‘iddah in the fifth month for a number of days equal to what she missed of the first month, whether the month was thirty days or twenty-nine days. 

See: al-Mughni, 8/85; Kashshaaf al-Qinaa‘, 5/418; al-Mawsoo‘ah al-Fiqhiyyah, 29/315 

Based on the above, if the ‘iddah began on 6/4/2012 (6 April 2012), which corresponds to 14 Jumaada al-Oola 1433, then the ‘iddah ends on 24 Ramadan 1433, which corresponds to 12 August 2012.  

And Allah knows best.