Once you have the midpoint, combine it with the given slope $-\dfrac{3}{4}$ in point-slope form: $y - y_1 = m(x - x_1)$.

At the $x$-intercept, what is the $y$-value? Substitute that value of $y$ into your line equation and solve for $x$.

The line goes through $(2,4)$ and has a negative slope. As $y$ decreases from $4$ down to $0$, should $x$ get bigger or smaller? Use this to check if your final $x$-value is reasonable.

In one expression line, type (6+(-2))/2 and in another type (-2+10)/2. Desmos will show 2 and 4, so the midpoint is $(2,4)$.

Enter the equation y-4 = (-3/4)(x-2) in Desmos. It will automatically graph the line that has slope $-3/4$ and passes through $(2,4)$.

Add the equation y=0 to show the $x$-axis clearly. Click (or tap) the point where the line intersects the $x$-axis. Read the $x$-coordinate of that intersection point; that value is the $x$-intercept.

The endpoints are $(6,-2)$ and $(-2,10)$. The midpoint formula is

So the midpoint is

This point lies on the line.

We know the slope is $m=-\dfrac{3}{4}$ and the line passes through $(2,4)$. Use point-slope form:

Substitute $m=-\dfrac{3}{4}$ and $(x_1,y_1)=(2,4)$:

This is an equation of the line.

The $x$-intercept is where the line crosses the $x$-axis, so $y=0$.

Set $y=0$ in the equation:

so

Multiply both sides by $4$:

Divide both sides by $-3$:

Add $2$ (which is $\dfrac{6}{3}$) to both sides:

So the $x$-intercept of the line is $\dfrac{22}{3}$.