Hi students,
I am Vinod Shankaran Sir. I teach English at Gradeup. I will share important observations that I have made in my years of teaching. Ask your queries here. I will endeavour to answer them.

Leaving ‘that’:
a) In sentences where ‘that’ is the object(pronoun) of the second clause:
• Here is the book you gave me (that book)
• I sold the book ABC refused to publish.
b) We can omit ‘that’ after the verb ‘say’ (that as a conjunction)
• She said her brother was coming to pick her up.
• The government says it has no plans of repealing the order.
c) If there is a subordinate noun clause (answering ‘what?)
• She says she will be late. (she says what?)
• I asked him why he was late. (I asked him what?)
• He hopes she would recognize him( he hopes what?)
• She wished she knew how to swim( she wished what?)
Don’t leave out ‘that’:
d) When adverbs come after the verb:
• He uttered excitedly that he had won the first prize.
• He told me two days ago that he would not be able to attend the party.
• We decided yesterday that we would go to the Himalayas.
e) After these verbs:
• Advocate, assert, contend, declare, estimate, make clear, point out, propose, state, agree, assume, calculate, conceive, hold, learn, maintain, suggest (and their synonyms)

f) When clauses start with subordinating conjunctions, use ‘that’
• I told him that after he had dropped unconscious, his parents came to visit him.
• We are of the opinion that although it is raining heavily, we have to move on.
**Finally there is no hard and fast rule for leaving out ‘that’. It is better to leave the ‘that’ in place rather than leave it and have confusion cropping up.