To solve for [tex]\((h \circ h)(10)\)[/tex], we need to understand what the composition of the function [tex]\(h\)[/tex] means. The notation [tex]\((h \circ h)(x)\)[/tex] represents the composition of the function [tex]\(h\)[/tex] with itself, evaluated at [tex]\(x\)[/tex]. In other words, it means that we first apply the function [tex]\(h\)[/tex] to [tex]\(x\)[/tex], and then apply [tex]\(h\)[/tex] again to the result.
Given that [tex]\(h(x) = 6 - x\)[/tex], let's go through the steps methodically:
1. Evaluate [tex]\(h(10)\)[/tex]:
[tex]\[
h(10) = 6 - 10 = -4
\][/tex]
2. Apply [tex]\(h\)[/tex] to the result of [tex]\(h(10)\)[/tex]:
[tex]\[
h(h(10)) = h(-4)
\][/tex]
3. Evaluate [tex]\(h(-4)\)[/tex]:
[tex]\[
h(-4) = 6 - (-4) = 6 + 4 = 10
\][/tex]
Thus, the value of [tex]\((h \circ h)(10)\)[/tex] is 10.
Therefore, the correct answer is:
[tex]\[
\boxed{10}
\][/tex]
