The above tableau is by far the most popular form used during the Durga Puja.
The story behind this scene is best described in the book Bengali Myths by T Richard Blurton (2006). Reproduced here, with appropriate thanks to the author and the publishers.
The iconography is distinctly Bengali, ten-armed Durga is flanked by Ganesha and Lakshmi on her right and Sarasvati and Karthikeya on her left. Bengali traditions (popular and folk) view the four, Ganesha, Lakshmi, Sarasvati and Karthikeya as Durga’s children. In no other region, Lakshmi and Sarasvati are considered Durga’s children. Strangely enough, Bengal’s classical tradition considers Lakshmi and Sarasvati to be Vishnu’s consorts.
Among Durga’s children, only Ganesha is shown with four arms and the other three have only two arms. Another oddity. though Mahisha is shown with a sword and a shield and the buffalo from which he emerges is not shown.
Despite the current popularity and de-facto use of this form, I have not come across any classical or pre-1600 depiction of this form, that is with the four children. The origin of this form and the basis for considering Lakshmi and Sarasvati as Durga’s children is not known.
One of the earliest recordings of this form is in the book Les Hindus by Balthazar Solvyns published in 1810. Reproduced here for educational purposes.
This form of Durga is an iconic image of India and was represented at the Great Exhibition 1851 and Paris exhibition Universelle 1855.
This monumental piece, an assembled one, is made using Dokhra techniques. Given the size (Height of 27 cm and width of 44 cm) it is quite an achievement. The Vigraha may be dated to the mid-twentieth century.
Photos below include a close-up view and a size comparison.