The gauge shows the tank is $\frac{3}{8}$ full. After adding 6 gallons, it reads $\frac{3}{4}$ full.

Fraction of tank filled by 6 gallons:

$\frac{3}{4} - \frac{3}{8} = \frac{6}{8} - \frac{3}{8} = \frac{3}{8}$

So $\frac{3}{8}$ of the tank $= 6$ gallons, meaning the full tank $= 16$ gallons.

A $\frac{3}{4}$-full tank contains:

$\frac{3}{4} \times 16 = 12 \text{ gallons}$

Total cost of gas in the tank:

$12 \times \$1.50 = \$18.00$