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Someone told me that according to Pirke de Rabbi Eliezer, Satan has 12 wings.

Is it true?

The tanakh doesn't say anything about Satan's look then where does it come from?

Yes Samael (the Satan) the accuser had 12 wings Yalkut Shimoni Bereishis 3,1:

אמרו מלאכי השרת לפני הקב"ה: "מה אדם ותדעהו? אדם להבל דמה"...והיה סמאל שר גדול בשמים, וחיות מארבע כנפים ושרפים משש כנפים וסמאל משתים עשרה.מה עשה סמאל? לקח כת שלו וירד

The angels said "whom is man that he should be known? man is futile".. Samael was greatest among those angels, the chayos had 4 wings, the _seraphim had 6 wings, yet Samael had 12 wings

The word "Satan"-שטן comes from the Passuk in Job 5,21: בשוט לשון תחבא -"From the accusing tongue hide away"(translation based on Rashi). This is Samael's undertaking, to be the accuser as evident from the Midrash above where he questions the very existence of man and wants G-d to do away with him. He then descends to earth as one of the fallen Angels most likely Azael see Nephilim after the Flood

The Pirkei Derabbi Eliezer 27 mentions that Samael was cast down from the heaven after his accusations against man, and that he tried to take down Michoel with him, but G-d cast him off and saved Michoel so Michoel is reffered to as the Polit (saved)
ולמה נקרא שמו פליט, שבשעה שהוריד הב"ה סמאל ואת כת שלו ממקום קדושתו מן השמים אחז בכנפיו של מיכאל להפילו עמו ופלטו הב"ה מידו לפיכך נקרא שמו פליט

Yes, it's true. It's found in Pirke de Rabbi Eliezer (Chapter 13):

והיה סמאל שר גדול בשמים, והחיות מארבע כנפים, ושרפים משש כנפים, וסמאל משנים עשר כנפים

Sammael was a great prince in heaven. The "Chayot" had four wings, the "Seraphim" had six wings, and "Sammael" had twelve wings.