To find the missing width of the rectangular prism, we can start with the formula for the surface area \( S \) of a rectangular prism, which is given by:
\[ S = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
Given:
- Length \( l = 6 \) cm
- Height \( h = 4 \) cm
- Surface area \( S = 188 \) cm²
We need to find the width \( w \).
Substituting the known values into the surface area formula, we have:
\[ 188 = 2(6w + 6 \cdot 4 + 4w) \]
Calculating the area of the sides that don’t involve \( w \):
\[ 188 = 2(6w + 24 + 4w) \]
Combine like terms:
\[ 188 = 2(10w + 24) \]
Now, divide both sides by 2 to simplify:
\[ 94 = 10w + 24 \]
Next, subtract 24 from both sides:
\[ 94 - 24 = 10w \]
\[ 70 = 10w \]
Now, divide both sides by 10 to solve for \( w \):
\[ w = \frac{70}{10} = 7 , \text{cm} \]
Thus, the missing width \( w \) of the rectangular prism is \( \boxed{7} \) cm.