I have started growing coriander and garlic chives on port inside house. Till four weeks after planting ,every thing grows well. but now I found all branches look very week and cannot stand firmly and falling apart. I would highly appreciate for any suggestion. I am giving water every 2 to 3 days, provided I check the soil if its dry once a day.
Germinating the seed in trays like your pictures is fine, but the seedlings should have been planted out to give them room to develop properly.
Both coriander and garlic chives plants grow to about 2 feet tall, and need to be spaced a few inches apart to develop properly. They need more depth of soil that a couple of inches in a seed tray as well.
Also trying to grow herbs indoors is usually a failure because the light levels are too low. These plants really need to be out of doors and getting direct sunlight for several hours each day. Even in "direct sun" indoors, a glass window can cut out up to 90% of the light compared with sunlight out of doors.
Garlic chives are frost hardy and are perennial plants, so they can be planted out of doors in the ground and will last for many years. Coriander is an annual (it grows, flowers, and dies within one year) so winter weather is not an issue anyway.
The most practical thing to do with the plants in your picture is just throw them away and start again. If you try to "rescue" them, they will never recover and develop properly.