Can we drive throut the forest from L.A. to San Francisco

There's no continuous route that connect Sequoia National Forest, Kings Canyon, and Yosemite to the north (well, unless you count the Pacific Crest Trail). You could drive the I-5/CA-99 corridor via Fresno and Modesto, cutting east as interest dictates to sites like Sequoia's General Sherman tree. Perhaps a better, more scenic option would be to drive US Highway 395 up toward Bishop, which puts to you to the east of the Sierra Nevadas and lets you gain some dramatic elevation as you head toward the ski twons of Mammoth Mountain and Mammoth Lakes, as well as scenic spots like Mono Lake. Access to Yosemite is by way of the dramatic drive across Tioga Pass on CA-120 by way of Lee Vining. Hope this helps!