The standard for of equation of a circle is
(x-a)²+(y-b)²=r²
where r is the radius of the circle and (a,b) is the center of the circle.
in x²+y²=25, the center is at (0,0). When the circle is translated 6 units left, it means that the new center has a=-6. Translating the circle 3 units down means that the new center has b=-2. So, the translated circle has the equation
(x+6)²+(x+3)²=25
Answer: (x+6)²+(x+3)²=25