Step 1: Check the Assertion using a faces-counting method instead of the cuboid formula.
Each cube of side $a=4$ cm has 6 faces of area $a^2$, so a single cube's total surface area is $6a^2$. When two cubes are joined end to end, one face from each cube gets glued together and hidden inside the solid.
Step 2: Subtract the hidden faces.
Two separate cubes together have combined area $2\times6a^2=12a^2$. Removing the two now-hidden faces:
\[ \text{TSA} = 12a^2-2a^2 = 10a^2 = 10\times4^2 = 160\text{ cm}^2 \]
This matches the Assertion, so Assertion (A) is true.
Step 3: Check the Reason by recalling why the factor of 2 appears in the standard formula.
A cuboid $l\times b\times h$ has three pairs of identical opposite faces: $l\times b$, $b\times h$, and $h\times l$, each pair contributing twice:
\[ \text{TSA} = 2(lb+bh+hl) \]
The Reason statement omits this factor of 2, counting each pair only once, so Reason (R) is false.
Step 4: Combine the two findings.
Assertion (A) is true, verified independently by the faces-counting method, but Reason (R) is false since it is missing the factor of 2.
Final Answer:
Since (A) is true and (R) is false, option (C) is correct.