During a solar eclipse, the Moon is in between the Earth and the Sun, but much, much closer to the Earth than the Sun.
The precise distance would depend upon where the Earth is in its orbit; at perihelion the Earth is about 146 million kilometers from the Sun, while at aphelion the Earth is about 152 million kilometers from the Sun. The average is precisely one AU, or about 149.6 million kilometers.
Then, it depends where the Moon is in its orbit around the Earth. At perigee the Moon is about 363,000 kilometers from the Earth; at apogee it is about 407,000 kilometers from the Earth. On average, it is about 384,000 kilometers away.
As you can see, the distance from the Moon to the Sun really doesn't depend all that much on where the Moon is relative to the Earth; it depends almost entirely on where the Earth is relative to the Sun. In this sense, the "during a solar eclipse" part is kind of redundant; even during a lunar eclipse the Moon would only be about 800,000 kilometers further away from the Sun, while the Earth's orbit can shift the distance by some 6,000,000 kilometers.
The minimum possible distance between the Moon and the Sun during a solar eclipse would be when the Moon is at apogee but the Earth is at perihelion; this would be 146,000,000 - 363,000 = 145.7 million km
The maximum possible distance would be when the Moon is at perigee but the Earth is at aphelion; this would be 152,000,000 - 407,000 = 151.6 million km
And the average distance between the Moon and the Sun would be 149,600,000 - 384,000 = 149.2 million km