What Is the best day to work with Hecate?
Thank you
Any day. She is the Greek goddess of magick itself.
However, timing generally depends on the purpose of the work being done, so you could plan it around the planetary hours. For example, she is often petitioned during specific moon phases, such as the full moon for necromancy, so Monday, the day of the moon, would work.
So would Wednesday, the day of Mercury/Hermes, as Hermes is a chthonic deity, like Hecate herself, capable of passing between realms, and they are often paired together, such as in the Hymn of Hecate in the Hesiod, as well as escorting Persephone between her seats of power in the underworld and Olympus.
Lastly, Saturday, the day of Saturn would also work.
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The New Moon, aka Deipnon.
(View source for Hecate - Wikipedia)
The Athenian Greeks honoured Hecate during the Deipnon. In Greek, deipnon means the evening meal, usually the largest meal of the day. Hecate’s Deipnon is, at its most basic, a meal served to Hecate and the restless dead once a lunar month[99] during the new moon. The Deipnon is always followed the next day by the Noumenia,[100] when the first sliver of the sunlit Moon is visible, and then the Agathos Daimon the day after that.
The main purpose of the Deipnon was to honour Hecate and to placate the souls in her wake who “longed for vengeance.”[101] A secondary purpose was to purify the household and to atone for bad deeds a household member may have committed that offended Hecate, causing her to withhold her favour from them. The Deipnon consists of three main parts: 1) the meal that was set out at a crossroads, usually in a shrine outside the entryway to the home[102] 2) an expiation sacrifice,[103] and 3) purification of the household.
I read any night of a dark moon.
If I remember correctly, November 16-18th are her festival days
In Greek Tradition August 13th and November 30th. Dark Moons Are Good Too & Fridays & Sundays too.
She loves Halloween night 
October 31st.