Yep - it can be mentioned that in 1. "to" is a preposition, not part of an infinitive, so a gerund has to follow.

1. The correct one. Look+ forward+ to + gerund. 4. The correct one. Without (prep) + gerund.

It would greatly appreciated if you could help me to point the one that is a sentence with correct grammar: 1. I look forward to hearing from you OR 2. I look forward to hear from you OR 3. I am looking forward to hear from you. 4.

If the sentence only contains these four words, it is incorrect. It needs a verb in there.

"nothing toward the goal". Is this sentence correct grammatically?

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