How do I know my prayers is answered?

Prayer is a two ways communication, not a monologue because for everything requested for needs an answer, you should understand that no problem or request is bigger than God
When your faith says so, you must receive it spiritually before it manifest physically, the world understand that it's seeing and believing but the Bible made it understandable that as a believer, it best we believe in it first because that's faith.

Matthew 21:22 (KJV) And all things, whatsoever ye shall ask in prayer, believing, ye shall receive.

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Until your faith says you have received, your hand can't receive, now the big question is 'what is your faith saying now'. When you pray, you should believe that you have received rather than having the spirit of doubt and that's what the devil wants, wanting you to generate a skeptical heart on your request.

When you no longer have that skeptical heart and give God the glory for the things not seen, rest assure that you prayers will be answered because that's what Faith is all about. You shouldn't worry about the ways and process that God is going to accomplish that your request, rather give him the thanksgiving.

Philippians 4:6 (KJV) Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God.

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We shouldn't be weak in faith and stagger not because staggering is unbelieving, be strong in God and give him all the Glory, God isn't intimidated by your request, be fully persuaded that your request has been answered rather than doubt. Pray, believing and start acting in line with your request, like you have gotten your request because that's what Faith teaches, in the time of creation, it was said that God starting calling those things like though it was there and they came to reality.

Let the teaching of faith abide in you because it will help enhance your blessings, remain blessed in Jesus name.