Sashtyabthapurthi' means completion of sixty years. This 'shanti' is performed for oneself on completion of 60 years and beginning of 61st year (61st birthday). Everyone including ladies can and should perform this 'shanti' to alleviate the sins committed so far and to re-charge our life.
As per Vedic scriptures, Human life is for 120 Years. Completion of sixty years means completing half-of-our full life. Tamil / Sanskrit years also have sixty year cycle.
In this function, poojas, japa and homams are done to numerous gods. Prominent amongst them are....Brahma, Vishnu, Rudra, mruthyunjaya parameswara, laxmy-narayana, navagrahas and naksatra devathas.
As per our scriptures, The following seven holy souls are called 'chiranjeevees', i.e. immortal souls. Remembering them brings good life.
Prayer is offered for them during this occasion.
Samvathsara devatas (60) i.e. Gods personifying all the sixty tamil / sanskrit years.
Nakshathra devatha (28) i.e. Gods personifying all the stars under the planet. Please note that veda mentions 28 stars, but in present day astrology we use only 27 stars.
Thithy devatha (15) i.e. Gods personifying the days of phase of the moon.
Navagrahas (9). Nine planets that rule and prescribe results for our karmas.
Dikpalakas (10) etc. i.e. Gods for ten directions.
We worship all the above gods at the completion of one's 60th birthday and the beginning of 61st birthday.
Generally, ekadasa rudra japam known as 'rudra-ekadasinee' (eleven rudra prayer *** homam) is also performed with mahanyasa, rudrabhishekam, kramarchana is also performed on the previous day of shashtiyabtha poorthi. This 'shaanthi' is the ultimate maha-prayashchitham and invokes the blessing of lord shiva.
In south india, during this occasion, we also recite the selected sacred mantras of marriage and the aged-couple re-take their marriage oath and invoke blessings for a long, happy and matured married life. This is an occasion when sons and daughters 'perform' the marriage of their parents!
The children sons and daughters must perform this shasti abdha poorthi function with their money only.