To find the missing width of the rectangular prism, we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 6 \) cm
- Height \( h = 4 \) cm
- Surface Area \( = 188 \) cm²
We need to find the width \( w \).
Substituting the known values into the surface area formula, we have:
\[ 188 = 2(6w + 6 \times 4 + 4w) \]
Calculating \( 6 \times 4 \):
\[ 6 \times 4 = 24 \]
Now substitute that back into the equation:
\[ 188 = 2(6w + 24 + 4w) \]
Combining like terms:
\[ 188 = 2(10w + 24) \]
Now divide both sides by 2:
\[ 94 = 10w + 24 \]
Next, isolate the term with \( w \) by subtracting 24 from both sides:
\[ 94 - 24 = 10w \]
\[ 70 = 10w \]
Now divide by 10:
\[ w = 7 \]
Thus, the missing width of the rectangular prism is 7 cm.