To determine which expressions are equivalent to [tex]\( 6g - 18h \)[/tex], let's simplify each given option and see if it matches [tex]\( 6g - 18h \)[/tex].
### Option A:
[tex]\[
(g - 3) \cdot 6
\][/tex]
Let's distribute the 6:
[tex]\[
(g - 3) \cdot 6 = 6g - 18
\][/tex]
This does not match [tex]\( 6g - 18h \)[/tex].
### Option B:
[tex]\[
2 \cdot (3g - 18h)
\][/tex]
Let's distribute the 2:
[tex]\[
2 \cdot (3g - 18h) = 6g - 36h
\][/tex]
This does not match [tex]\( 6g - 18h \)[/tex].
### Option C:
[tex]\[
3(2g - 6h)
\][/tex]
Let's distribute the 3:
[tex]\[
3(2g - 6h) = 6g - 18h
\][/tex]
This matches [tex]\( 6g - 18h \)[/tex].
### Option D:
[tex]\[
(-g - 3h)(-6)
\][/tex]
Let's distribute the [tex]\(-6\)[/tex]:
[tex]\[
(-g - 3h)(-6) = 6g + 18h
\][/tex]
This does not match [tex]\( 6g - 18h \)[/tex].
### Option E:
[tex]\[
-2 \times (-3g + 9h)
\][/tex]
Let's distribute the [tex]\(-2\)[/tex]:
[tex]\[
-2 \times (-3g + 9h) = 6g - 18h
\][/tex]
This matches [tex]\( 6g - 18h \)[/tex].
So, the two expressions that are equivalent to [tex]\( 6g - 18h \)[/tex] are:
C: [tex]\( 3(2g - 6h) \)[/tex] and E: [tex]\( -2 \times (-3g + 9h) \)[/tex]
