Dought & clear - , Working out the ‘iddah following the death of the husband according to the Hijri date

I want to find out when my mother's 'iddah will end. My father (may
Allah have mercy on him – I hope that you will pray for mercy and
forgiveness for him) died on Friday 6/4/2012.
Praise be to Allaah.
Firstly:
We ask Allah, may He be exalted, to have mercy on your father and
forgive him, and to havemercy on all the deceased Muslims, for Heis
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 beexalted, says (interpretation of the meaning):
"And those of you who die and leave wives behind them, they(the wives)
shall wait (asregards their marriage) for four months and ten days"
[al-Baqarah 2:234].
Thirdly:
The woman whose husband has died must observe 'iddah followingthe
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 anyof 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 'iddahin 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 themonth – 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 monthfor a number of days
equal to what she missed of the first month, whether the month was
thirty days ortwenty-nine days.