Separate and peel garlic cloves. (To facilitate, you can soak the separated cloves in enough warm water to cover for 1/2 hour). Cut the peeled cloves into broad, thin slices.
Place 12 tablespoons of the olive oil in a very wide saute pan or Dutch oven over medium-high heat. Add the sliced garlic, reserving about 4 cloves worth of slices for later. Cook, stirring occasionally, until garlic is almost brown (about 5 minutes).
While the garlic is cooking, place the contents of the 2 cans of tomatoes in a colander and, working over a sink, squeeze the tomatoes in your hands until the tomatoes are a coarse pulp.
When the garlic is almost brown, add tomatoes to the pan. Add 1/2 cup shredded basil. Cook over medium heat for 10 minutes, uncovered, then remove from heat and reserve.
Open the 12 large clams with a clam knife, reserving juice. Chop coarsely and reserve.
Add the spaghetti to a large pot of salted boiling water. Cook until al dente (about 10 minutes). When pasta is done, drain through colander. Toss the hot linguine in colander with a little olive oil.
Place the remaining 4 tablespoons of olive oil in the now empty pasta pot over high heat. Add the reserved 4 cloves of garlic cut in thin slices. Saute until almost brown. Add Manilla clams. Add another 1/2 cup of shredded basil. Add half of the reserved tomato sauce. Add a little bit of the reserved clam juice. Cover the pot and cook until the clams open. As soon as the clams open, add chopped clams and spaghetti. Mix well. Add additional sauce if desired. Add the remaining basil. Season to taste with salt and pepper. Turn out onto large pasta platter. Garnish with extra sprigs of basil. Serve immediately.
Suggested drink: Gai, Trebbiano dei Colli Martani, Rocca di Fabbri