Question

what is the Earth rotates how many longitudes face the sun daily

Answer 1

All of them. You can’t count longitude, as it is a continuous measure. But every day (as in 24 hours) the Earth turns through 360° of longitide, east to west, so every location of longitude experiences local solar noon.

Answer 2

It depends on how many lines you suppose to draw.

If you draw longitudes at one degree interval, you will get 360 lines and the lines face the sun 360 times daily.

If you draw longitudes at five degree interval, the lines will face the sun 72 times daily.

Here I conclude every line will face the sun in a day.