To find the total thickness of a stack of 54 sheets of metal, each 2/3 of an inch thick, we need to multiply the thickness of one sheet by the number of sheets.
We can calculate this as follows:
\[ \text{Total thickness} = \text{Number of sheets} \times \text{Thickness of one sheet} \]
Substituting the values:
\[ \text{Total thickness} = 54 \times \frac{2}{3} \]
To perform the multiplication, we proceed as follows:
\[ 54 \times \frac{2}{3} = \frac{54 \times 2}{3} \]
Calculating \(54 \times 2\):
\[ 54 \times 2 = 108 \]
Now we have:
\[ \frac{108}{3} \]
Next, we divide 108 by 3:
\[ 108 \div 3 = 36 \]
Thus, the total thickness of the stack of sheets is:
\[ \boxed{36} \text{ inches} \]