Step 1: Build the cuboid by adding up its six faces one at a time, instead of using the total surface area formula.
Joining two cubes of side 4 cm end to end gives a cuboid of length $l = 8$ cm, breadth $b = 4$ cm, and height $h = 4$ cm. A cuboid has 3 pairs of identical opposite faces:
Top and bottom faces: each measures $l \times b = 8 \times 4 = 32$ cm$^2$, giving $2 \times 32 = 64$ cm$^2$.
Front and back faces: each measures $l \times h = 8 \times 4 = 32$ cm$^2$, giving $2 \times 32 = 64$ cm$^2$.
Left and right faces: each measures $b \times h = 4 \times 4 = 16$ cm$^2$, giving $2 \times 16 = 32$ cm$^2$.
Step 2: Add all six faces to get the total surface area.
\[ \text{Total Surface Area} = 64 + 64 + 32 = 160 \text{ cm}^2 \]
This matches the value given in Assertion (A), so Assertion (A) is true.
Step 3: Test Reason (R) by plugging its own numbers in and comparing to the real answer.
Reason (R) claims the surface area equals $lb + bh + hl$. Plug in the same dimensions:
\[ lb + bh + hl = (8)(4) + (4)(4) + (4)(8) = 32 + 16 + 32 = 80 \text{ cm}^2 \]
This gives 80 cm$^2$, but the actual surface area worked out in Step 2 is 160 cm$^2$. Since $80 \neq 160$, the formula in Reason (R) does not give the correct surface area value, so Reason (R) is false (it is missing the factor of 2 that turns it into the correct total).
Step 4: Final Answer.
Assertion (A) is true, but Reason (R) is false, so option (C) is correct.
\[ \boxed{\text{A is true, R is false}} \]