Peel the radish skin and chop them in small pieces and microwave it for 10 minutes. Do not overcook them.
Similarly peel the carrot skin and microwave it for 6 minutes and then chop them. Par-boiled carrots are easy to chop.
Heat the kadai and add oil.
Once the oil is hot add mustard seeds, urad dal and channa dal.
When they start spluttering add dried red chillies and hing.
Fry them for a minute.
Add the boiled veggies and salt.
Mix them well, once the water(if any) is all evaporated add the coconut.
Let it cook for couple minutes in low heat and thats it, the poriyal is ready.
Notes
You can steam both radish and carrot together but sometimes the color of the carrot mixes with radish too. So I prefer steam them separately. If you want to skip the use of microwave, you can chop the veggies and steam them on stove top. After the tempering part, you can add the chopped veggies and salt and about ¼ cup of water and cover and cook till they become tender. Adjust the salt and spices according to your preference.