To find the reaction at the nearest support of a simply supported beam with an overhang, follow these steps:

Given:

• Span of simply supported beam, \(L = 6\, \text{m}\)
• Overhang length, \(L_{\text{overhang}} = 4\, \text{m}\)
• Uniformly Distributed Load (UDL) on overhang = \(6\, \text{kN/m}\)

Steps to solve:

1. Calculate the total UDL acting on the overhang:

The total load \(W_{\text{total}}\) acting on the overhang is given by:\)

1. Find the equivalent point load due to the UDL:

The equivalent point load acts at the midpoint of the overhang, which is \(2\, \text{m}\) from the end of the overhang.

1. Calculate the moment about the nearest support (point A):

Let the reaction at the nearest support be \(R_A\). Taking moments about point A (the nearest support):

\(R_A \times 0 = W_{\text{total}} \times ( \text{L} + ( L_{\text{overhang}}/2 ) )\), 
\(R_A \times 0 = 24 \times (6 + 2)\) 
\(R_A = \frac{24 \times 8}{6} = 32 \, \text{kN}\)

1. Conclude the reaction at the nearest support:

Therefore, the reaction at the nearest support (point A) is \(32 \, \text{kN}\).

Conclusion:

The correct answer is 32 kN.

Hence, the reaction at the nearest support is 32 kN.