Select the correct answer.

A construction company is analyzing which of its older projects need renovation. Building B was built two years before Building C. Building D was built two years before Building B. The product of Building B's age and Building D's age is at least 195. If [tex]x[/tex] represents the age of Building C, which inequality represents this situation?

A. [tex]x^2+4x+4 \geq 195[/tex]
B. [tex]x^2+6x+8 \geq 195[/tex]
C. [tex]x^2+4 \geq 195[/tex]
D. [tex]x^2+8x+16 \geq 195[/tex]

Let [tex]$x$[/tex] represent the age of building [tex]$C$[/tex]. According to the problem:

1. Building [tex]$B$[/tex] was built two years before building [tex]$C$[/tex]. Therefore, the age of building [tex]$B$[/tex] is
[tex]$$x + 2.$$[/tex]

2. Building [tex]$D$[/tex] was built two years before building [tex]$B$[/tex]. Thus, the age of building [tex]$D$[/tex] is
[tex]$$(x + 2) + 2 = x + 4.$$[/tex]

3. The product of the ages of buildings [tex]$B$[/tex] and [tex]$D$[/tex] is at least 195. This gives the inequality:
[tex]$$ (x + 2)(x + 4) \geq 195. $$[/tex]

4. Expanding the left-hand side, we have:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8.
\][/tex]

So, the inequality becomes:
[tex]$$ x^2 + 6x + 8 \geq 195. $$[/tex]

5. This expression matches option B.

Thus, the correct answer is:

[tex]$$\boxed{x^2 + 6x + 8 \geq 195.}$$[/tex]