The correct answer is $\boxed{\text{C) 119}}$.
The output of a neuron is calculated by multiplying the inputs by the weights and then adding them together. In this case, the inputs are 4, 10, 5, and 20, and the weights are 1, 2, 3, and 4. So, the output is $4 \times 1 + 10 \times 2 + 5 \times 3 + 20 \times 4 = 119$.
The transfer function is a mathematical function that maps the inputs to the output. In this case, the transfer function is linear, which means that the output is proportional to the inputs. The constant of proportionality is 2, so the output is $2 \times (4 + 10 + 5 + 20) = 119$.
Option A is incorrect because it is the sum of the inputs, which is 40. Option B is incorrect because it is the product of the inputs, which is 800. Option D is incorrect because it is the sum of the weights, which is 10.