Let's denote the hours Sheldon babysat on Saturday as \( x \).
Sheldon earns $4 per hour. Therefore, his earnings from babysitting on Saturday can be expressed as:
\[ 4x \]
On Sunday, he babysat for 8 hours. His earnings for Sunday would then be:
\[ 4 \times 8 = 32 \]
Now, according to the information provided, the total amount he earned over the weekend is $56. We can set up the following equation:
\[ 4x + 32 = 56 \]
To find \( x \), we first subtract 32 from both sides:
\[ 4x = 56 - 32 \] \[ 4x = 24 \]
Next, we divide both sides by 4:
\[ x = \frac{24}{4} = 6 \]
So, Sheldon babysat for 6 hours on Saturday.
In conclusion, the answer is:
\[ \text{Sheldon babysat for 6 hours on Saturday.} \]