The isoquants of the production function are right-angled; the corner of the y-isoquant is at the point (y,2y). (If you have y units of input 1 and 2y units of input 2 then you can efficiently produce y units of output.)
Thus to produce any output y the cost-minimizing input bundle is (y,2y). Thus the firm's cost function is TC(y,w1,w2) = w1y + 2w2y = (w1 +
2w2)y.