We are asked to simplify the expression $3x(7y - 4z)$. This involves applying the distributive property.

1. Problem Description

We are asked to simplify the expression $3x(7y - 4z)$. This involves applying the distributive property.

2. Solution Steps

We need to distribute the term $3x$ to both terms inside the parentheses.

The distributive property is $a(b+c) = ab + ac$.

$3x(7y - 4z) = (3x)(7y) - (3x)(4z)$

Now we multiply the coefficients and variables in each term.

$(3x)(7y) = 3 \times 7 \times x \times y = 21xy$

$(3x)(4z) = 3 \times 4 \times x \times z = 12xz$

Therefore, $3x(7y - 4z) = 21xy - 12xz$.

3. Final Answer

$21xy - 12xz$