smc

Write each equation in slope-intercept from since the slopes are easier to compare. Equation $(1)$ in slope-intercept form is $y=\frac{2}{3}x+4$. Equation $(2)$ in slope-intercept form is $y=-\frac{2}{3}x-\frac{10}{3}$. Equation $(3)$ in slope-intercept form is $y=-\frac{2}{3}x+4$. Equation $(4)$ in slope-intercept form is $y=-\frac{3}{2}x+5$. Remember that if the two lines are perpendicular, then the product of two slopes equals $-1$. Equations $(1)$ and $(4)$ satisfy the condition, so the answer is $\boxed{\text{(1) and (4)}}$.