The set A = {x:x ∈ R, x2 = 16 and 2x = 6} equals
{14, 3, 4}
{3}
{4}
x2 = 16 ⇒ x = ± 4
2x = 6 ⇒x=3
There is no value of x which satisfies both the above equations.
Thus, A = ∅.