Prophet of Allah صلی اللہ علیہ وسلم said:

The invocation of any of you is granted (by Allah) if he does not show impatience (by saying, I invoked Allah but my request has not been granted.)

[Sahih Bukhari 6340]

There are 3 forms in which a dua is accepted.

Prophet of Allah صلی اللہ علیہ وسلم said:

Any Muslim who makes a supplication containing nothing which is sinful, or which involves breaking ties of relationship, will be given for it by Allah one of three things:

1️⃣ He will give him  a swift answer,

2️⃣ or store it up for him in the Hereafter,

3️⃣ or turn away from him an equivalent amount of evil.”

[Mishkat al Masabih 2259]

The First Form of Acceptance of Dua:

If a person makes dua to ask for something or to request removal of a difficulty or an obstacle, the first form of acceptance of dua is that either his wish is fulfilled or his problem is resolved.

If your dua is answered, be grateful to Allah. Try to be even more righteous than before and praise Him more than before.

وَأَمَّا بِنِعْمَةِ رَبِّكَ فَحَدِّثْ

♦️And proclaim the blessings of your Lord.

[Ad-Duhaa 93:11]

Unfortunately, the normal practice is that when our duas and prayers have been answered, we forget the issues that were troubling us before and tend to forget to be thankful to Allah Almighty, the One who had taken us out of our misery. Instead of being grateful to Him, we forget all our promises to Him and start walking on the path of sin once again.

وَاِذَاۤ اَنۡعَمۡنَا عَلَى الۡاِنۡسَانِ اَعۡرَضَ وَنَاٰ بِجَانِبِهٖ​ۚ وَاِذَا مَسَّهُ الشَّرُّ فَذُوۡ دُعَآءٍ عَرِيۡضٍ‏ 

♦️When We show favour to someone, they turn away, acting arrogantly. And when touched with evil, they make endless prayers ˹for good˺.

[Fussilat 41:51]

The Second Form of Acceptance of Dua:

The second form of acceptance of dua is that when a person makes dua for the removal of a difficulty that he is facing, the difficulty remains the same, but the major catastrophe that was to follow it, is removed. 

We should never say that Allah Almighty has not answered our prayers.

Allah Almighty can answer our prayers in different forms. For example, you make dua to improve your business, but are bestowed with righteous offspring instead.

Allah Almighty always answers our duas, but the form in which the dua is answered, we sometimes fail to understand it. We should strongly believe that all of our prayers would be answered إنشاءاللّٰه .

Prophet of Allah صلی اللہ علیہ وسلم said:

When a person leaves a thing to avoid disobedience of Allah, then he is bestowed with a far better thing by Allah Almighty.

Musnad Ahmed]

The Third Form of Acceptance of Dua:

On the Day of Judgement, a person would be given his due share of reward for his good deeds. After his whole life has been accounted for, he would see a huge mountain of rewards, which would be bestowed on him. He would ask:

“O Lord! Where did this reward come from?”

The Lord would answer him:

“The rest was your reward for the virtuous deeds that you did. This reward is for all the unfulfilled duas that you made in your life.”

That person would see such huge favour and would feel regretful and would think that it would have been better if none of his duas were answered in this life.