To subtract $-4$ from $4$, we combine the two negative signs to make a single plus sign. This gives

\begin{align*} 4-(-4) &= \\[5pt] 4+4 &= \\[5pt] 8 &. \end{align*}

To subtract $-30$ from $5,$ we combine the two negative signs to make a single plus sign. This gives

\begin{align*} 5-(-30) &= \\[5pt] 5+30 &= \\[5pt] 35&. \end{align*}

To subtract $-5$ from $-5,$ we combine the two negative signs to make a single plus sign. This gives

\begin{align*} -5-(-5)&= \\[5pt] -5+5 &= \\[5pt] 0&. \end{align*}

To subtract $-25$ from $-45$, we combine the two negative signs to make a single plus sign. This gives

\begin{align*} -45-(-25) &= \\[5pt] -45+25 &= \\[5pt] -20&. \end{align*}

To subtract $-3.5$ from $5$, we combine the two negative signs to make a single plus sign. This gives

\begin{align*} 5-(-3.5) = 5+3.5. \end{align*}

To calculate $5+3.5$, we start at $5$ and move $3$ places to the right. Then, we move another $0.5$ places to the right:

Thus, \[ 5-(-3.5)=8.5. \]

To subtract $-4.5$ from $3.5$, we first combine the two negative signs to make a single plus sign:

\begin{align*} 3.5-(-4.5)= 3.5+4.5&. \end{align*}

So, we start at $3.5$ and move $4$ places to the right. Then, we move another $0.5$ places to the right.

Thus,

\begin{align*} 3.5-(-4.5) = 8&. \end{align*}

To subtract $-\dfrac{6}{5}$ from $-\dfrac{2}{5}$, we first combine the two negative signs to make a single plus sign. This gives

\begin{align*} -\dfrac{2}{5}-\left(-\dfrac{6}{5}\right) = -\dfrac{2}{5}+ \dfrac{6}{5}. \end{align*}

We have a common denominator of $5$, so we combine the numerators:

\begin{align*} -\dfrac{2}{5} + \dfrac{6}{5}= \dfrac{-2+6}{5}. \end{align*}

Finally, we work out $-2+6$ using our number line.

Hence, $ \dfrac{-2+6}{5} = \dfrac{4}{5} .$

To subtract $-\dfrac{2}{3}$ from $\dfrac{1}{6}$, we drop the parentheses and combine the two negative signs to make a single plus sign:

\begin{align*} \dfrac{1}{6}-\left(-\dfrac{2}{3}\right)= \dfrac{1}{6} +\dfrac{2}{3}&. \end{align*}

Now, we express the two numbers as fractions over a common denominator of $6$ and combine the numerators. This gives

\begin{align*} \dfrac{1}{6}+\dfrac{2}{3} = \dfrac{1}{6}+\dfrac{4}{6}= \dfrac{1+4}{6}&. \end{align*}

Next, we work out $1+4$ using our number line.

So we get

\[\dfrac{1+4}{6} = \dfrac{5}{6}.\]