If 16^2 − k = (4y + 3/2)( 4y − 3/2), then the value of k is:

$16^2 − k = (4y + \frac{3}{2})( 4y − \frac{3}{2})$

= a² – b² = (a - b) (a + b)------(1)

$16^2 − k = (4y )^2 -  (\frac{3}{2}^2)$

16² - k = 16y² - $(\frac{9}{4})$------(2)

comparing (2) with (1) we get,

k = $(\frac{9}{4})$