1. I wish for you that, with every year, you achieve all of your dreams.

[Is it grammatical? Do we have to delete 'for'?]

2. You’re supposed to let go of the past and start off new.
[Do we have to put 'the ' before 'new'?]

1. I wish for you that, with every year, you achieve all of your dreams.

[Is it grammatical? Do we have to delete 'for'?]

2. You are supposed to let go of the past and start off new.
[Do we have to put 'the ' before 'new'?]

1. I wish for you that, with every year, you achieve all of your dreams.

[Is it grammatical? Do we have to delete 'for'?]
Yes, this sentence is grammatically correct, and you need to keep "for" in this phrasing. I'd use "reach" in place of "achieve," though.

2. You are supposed to let go of the past and start off new.
[Do we have to put 'the ' before 'new'?]
No, no need for "the" before "new."

1. The sentence "I wish for you that, with every year, you achieve all of your dreams" is grammatically correct. You do not need to delete the word "for." The phrase "wish for" is a common expression that means to desire or hope for something to happen for someone else.

2. The sentence "You’re supposed to let go of the past and start off new" should be written as "You're supposed to let go of the past and start off anew." In this case, the word "the" is not necessary before "new." The word "anew" means in a new or different way, suggesting a fresh start.

1. The given sentence "I wish for you that, with every year, you achieve all of your dreams" is indeed grammatically correct. The word "for" in this context shows the verb "wish" requires a receiver or beneficiary. Hence, it is not necessary to delete the word "for" in this sentence.

2. The sentence "You're supposed to let go of the past and start off new" is grammatically correct, but there is no need to include the article "the" before "new" in this sentence. "Start off new" is a common phrase used to express the beginning of something fresh or different, and it does not require the definite article "the."