To determine the total time Henry spends commuting to and from school each day, we need to combine the expressions representing the time to and from school.
The time taken to get to school is given by:
[tex]\[ x - 8y \][/tex]
The time taken to get from school is given by:
[tex]\[ 2x - 4y \][/tex]
To find the total commuting time, we simply add the two expressions together:
[tex]\[ (x - 8y) + (2x - 4y) \][/tex]
Now, let's combine the like terms. First, combine the terms with [tex]\(x\)[/tex]:
[tex]\[ x + 2x = 3x \][/tex]
Next, combine the terms with [tex]\(y\)[/tex]:
[tex]\[ -8y - 4y = -12y \][/tex]
Putting it all together, we get:
[tex]\[ 3x - 12y \][/tex]
So, the expression that represents the total time Henry spends commuting to and from school each day is:
[tex]\[ 3x - 12y \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{3x - 12y} \][/tex]
