I heard that the Prophet, sallallaahu ‘alayhi wa sallam, recommended using the following formula to get your wishes realized:
1) Recite Salawaat (invoke the blessings of Allah on the Prophet) 11 times.
2) Recite "Hasbiyallahu laa Ilaaha illa Huwa alayhi..." 7 times.
3) Recite Salawaat 11 times.
4) State your wish and Allah will grant it.
I wanted to learn more about the above-mentioned recommendation of the Prophet.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

After careful research, we could not find a prophetic command to recite Salawaat eleven times in particular. However, reciting Salawaat has a great effect in the acceptance of supplications. A Muslim should frequently invoke the blessings of Allah on the Prophet, sallallaahu ‘alayhi wa sallam, as much as he can. The Prophet, sallallaahu ‘alayhi wa sallam, said, "Every supplication is screened until blessings are invoked upon Muhammad, sallallaahu ‘alayhi wa sallam." [At-Tabaraani and Al-Bayhaqi; Al-Albaani: authentic]

Moreover, Fudhaalah ibn ʻUbayd, may Allah be pleased with him, narrated that the Messenger of Allah, sallallaahu ‘alayhi wa sallam, heard someone supplicating after his prayer without praising Allah and without invoking the blessings of Allah upon the Prophet, sallallaahu ‘alayhi wa sallam. So he said, "This man has rushed (into the supplication)." Then he called him and said, "When one of you supplicates, let him start by praising his Lord, the Exalted, and glorifying Him, then invoke blessings upon the Prophet. Then he may supplicate with whatever he wishes." [Abu Daawood, At-Tirmithi, and An-Nasaa'i]

Ubayy ibn Kaʻb, may Allah be pleased with him, said, "O Messenger of Allah, I frequently invoke the blessings of Allah upon you. How much of my supplications should I devote to you?" He, sallallaahu ‘alayhi wa sallam, said, "Whatever you wish." I said, "A quarter?" He said, "Whatever you wish, and if you do more, it is better for you." I said, "One half?" He said, "Whatever you wish, and if you do more, it is better for you." I said, "Two thirds?" He said, "Whatever you wish, and if you do more, it is better for you." I said, "Shall I devote all my supplication to (invoking blessings upon) you?" He said, "Then, you will be freed from your worry and your sin will be forgiven." [At-Tirmithi: good-authentic; Al-Haakim in Al-Mustadrak]

Shaykh Al-Islam Ibn Taymiyyah wrote, "The hadith reads, 'Then, you will be freed from your worry and your sin will be forgiven.' The other version of the hadith reads, 'Then, Allah will free you from what worries you of the matters of this worldly life and the Hereafter.' This is the ultimate objective of a person's supplications regarding bringing forth all that is good and warding off all evils." [Majmooʻ Al-Fataawa]

As for reciting the Thikr (expressions of remembrance of Allah), "Hasbiyallahu laa Ilaaha illa Huwa..." we could not find any hadith indicating that it is a reason for the acceptance of supplication. However, it was authentically reported that this Thikr should be recited seven times in the morning and evening and that, as a reward, the reciter will be freed from his worries related to the worldly life and the Hereafter.

The Prophet, sallallaahu ‘alayhi wa sallam, said, "Whoever says seven times in the morning and evening, 'Hasbiyallaahu laa Ilaaha illa Huwa ʻAlayhi Tawakkaltu wa Huwa Rabbul-ʻArsh Al-ʻAtheem (which means: Sufficient for me is Allah; there is no god but He; on Him I rely, and He is the Lord of the Glorious Throne),' Allah will suffice him against anything which grieves him in this worldly life or the Hereafter." [Ibn As-Sunni] Al-Arnaa’oot declared it authentic in his revision of Zaad Al-Maʻaad.

Allah knows best.