Correct spelling, explaination: in cases when a word ends with consonant-vowel-consonant we, in most cases, double the last consonant when adding -ing or -ed ending. This is why the correct gerund form of put is putting, not puting.

Definition of putting:
verb, gerund of put, to set or place something somewhere
It’s very rainy today; putting on a raincoat is a good idea.
Please stop putting your feet on the table!

Incorrect spelling, explaination: verbs that end with the combination consonant-vowel-consonant double their last consonant in cases of adding -ed or -ing form to them. Some examples of this are: rob→ robbed, sit → sitting. The same applies to put, so the correct form here is putting and not puting.