The grass
a. cut b. to cut c. cutting d. be cut

- - The grass needs cutting.

Your answer is C because if you were to read these out loud, its the only one that makes sense.

The grass needs cut
The grass needs to cut
The grass needs cutting
The grass needs be cut

See what I mean?

Final C

The grammatically correct sentence would be C.
The grass needs cutting.
The rest are grammatically incorrect as follows. :)
Cut, is used more for future tense or past tense in general.
To cut, is an infinitive which when defining that we can determine is not needed in the sentence.
Be cut, is future tense and our sentence is present tense.
Cutting, is not only present tense, the correct tense, an action 'ing' word but it is also a gerund which completes the sentence accurately.

Hope this helped! If you need anymore help, have any other questions or need further explanation just let me know!! :)