While answering the math, geometry, pattern and some other puzzling, in case if I faced some difficulty to explain my answer by typing, can I write/draw the answer in the paper, taking that as a photo and add a picture to the answer is allowable?
That is certainly allowable, but it's not an ideal solution. If there is a picture or diagram you want to include as part of your answer, then definitely insert it as an image, but I would encourage you to type as much as possible of it as text.
Doing so helps the answer to be more searchable, and most of the time will be much easier to read. It also lets you or someone else edit your answer if something needs to be changed or clarified.
For mathematical notation, you can use MathJax to construct just about any mathematical equation or construct.
If you don't feel capable of anything but posting a single image with the entire answer, I'd say that's still better than nothing, but far from ideal.
You can of course click a picture of a handmade diagram to explain the answer well. But you need to type the plain text. You cannot post the picture of a plain text because:
some users might not be able to understand your handwriting.
the webpage will take time to load and it will create annoyance for other users.
(half jokingly) save trees?
I do agree with both the answers written.
I'd like to add one more point that while adding a picture shows your homework/effort on the question, you must make sure that others are able to understand your approach towards the given question(not that my handwriting is so bad). Thus adding lines of text explaining your idea makes it easier for fellow puzzlers to comprehend your thoughts :)