What it is
Dwadashamsha divides each sign into twelve equal parts of 2°30′. Its charm is that the whole zodiac turns once inside every sign: the first part belongs to the sign itself and the last to the 12th sign from it.
How it is calculated
Rule: the count starts from the same sign and runs through the twelve signs in order.
Example: a planet is at Aries 17°. 17 ÷ 2.5 = 6.8, so the seventh part. The seventh sign from Aries is Libra, so in D12 the planet is in Libra.
What tradition looks at in it
Parāśara links the dwadashamsha to parents. Tradition reads the Sun as the significator of the father and the Moon of the mother, along with the lords of the 4th house (mother) and the 9th (father; some traditions also use the 10th). It is taken as a view of the values, support and bond one receives from one's parents.
How much the birth time matters
On average the ascendant moves about 1 degree every 4 minutes; some signs rise faster, some slower. One part of D12 is 2°30′, so a difference of roughly 10 minutes in birth time can change the D12 ascendant. The Moon crosses one part in about 4–5 hours. In your chart, ePandit shows next to every varga how many minutes of birth-time change would shift its ascendant. Read the D12 ascendant only when the birth time is reliable.
How to read it calmly
Read D12 as a second look, not a verdict. Tradition first studies the 4th and 9th houses and their lords in the main chart (D1), then the running dasha. D12 only helps check whether the same theme shows up here as well. A planet's sign in this varga decides nothing on its own. Draw no conclusions about a parent's health from a chart; for health, the doctor is the first support.