## Answer :

[tex]\[ (a \times b) \times c = a \times (b \times c) \][/tex]

Now, let's analyze each option to see which one illustrates this property:

**Option A:**

[tex]\[ 23 \times (4 \times 31) = (4 \times 31) \times 23 \][/tex]

This option reorders the factors but does not regroup them differently on both sides of the equation. Therefore, this does not reflect the associative property.

**Option B:**

[tex]\[ 46 \times 1 = 46 \][/tex]

This option represents the identity property of multiplication, which states that any number multiplied by 1 remains unchanged. This is not related to the associative property.

**Option C:**

[tex]\[ 16 \times 31 = 16(30 + 1) \][/tex]

This option utilizes the distributive property of multiplication, which involves distributing the multiplication over addition. It does not exhibit the associative property.

**Option D:**

[tex]\[ 24 \times (4 \times 51) = (24 \times 4) \times 51 \][/tex]

This option shows that the grouping of factors is reassigned in accordance with the associative property. The left-hand side groups 4 and 51 together first, while the right-hand side groups 24 and 4 together first before multiplying by 51. This conforms to the property:

[tex]\[ (a \times b) \times c = a \times (b \times c) \][/tex]

Hence, the correct equation showing the associative property of multiplication is:

[tex]\[ D. \quad 24 \times (4 \times 51) = (24 \times 4) \times 51 \][/tex]