4. Using algebraic rules, find the value of \( k \) for which \( 58^{2}-46^{2}=12 k \) \[ \begin{aligned} 58^{2} & =60^{2}-2^{2} \\ & =3600-4 \\ & =3596\end{aligned} \]

We can simplify the expression \(58^{2}-46^{2}\) by using the difference of squares formula: \[ a^{2}-b^{2}=(a-b)(a+b) \] Let \(a=58\) and \(b=46\). Then: \[ 58^{2}-46^{2} = (58-46)(58+46) \] Calculate the differences and sums: \[ 58-46 = 12 \quad \text{and} \quad 58+46 = 104 \] Substitute these back into the expression: \[ 58^{2}-46^{2} = 12 \times 104 = 1248 \] We are given that: \[ 58^{2}-46^{2}=12k \] Thus, equate: \[ 12k = 1248 \] Solve for \(k\) by dividing both sides by 12: \[ k=\frac{1248}{12}=104 \] So, the value of \(k\) is \(\boxed{104}\).