Handwritten math problem on a whiteboard involving hot dogs and a coupon discount.

To find the value of $h$ (the price of one hot dog), we need to solve the equation step by step.

Step 1: Write down the equation.
$$3h - 0.75 = 4.80$$

Step 2: Isolate the term with $h$.
We want to get $3h$ by itself on the left side. To do this, we need to remove the $-0.75$. We can do this by adding $0.75$ to both sides of the equation.

$$3h = 4.80 + 0.75$$

Let's do the addition:
$$4.80 + 0.75 = 5.55$$

So now the equation is:
$$3h = 5.55$$

Step 3: Solve for $h$.
Now we have $3$ times $h$ equals $5.55$. To find just $h$, we need to divide both sides by $3$.

$$h = \frac{5.55}{3}$$

Let's do the division:
- $5 \div 3 = 1$ with a remainder of $2$.
- Bring down the $5$ to make $25$. $25 \div 3 = 8$ with a remainder of $1$.
- Bring down the last $5$ to make $15$. $15 \div 3 = 5$.

So, $5.55 \div 3 = 1.85$.

$$h = 1.85$$

Verification:
If each hot dog costs $\$1.85$:
- 3 hot dogs cost $3 \times 1.85 = \$5.55$.
- Subtract the $\$0.75$ coupon: $5.55 - 0.75 = \$4.80$.
This matches the total price given in the problem.

Final Answer:
h = 1.85